The call comes one week after his deputy, Nicola Sturgeon, revealed that taxpayers' cash was spent to keep the public from knowing that no "specific" legal advice had been taken in the first place.
Mr Salmond was accused of being a "barefaced liar" as opposition MSPs insisted that the SNP leader gave the impression in a television interview that advice existed to back the assertion that Scotland would automatically remain in the EU after a Yes vote in 2014.
Labour leader Johann Lamont has now deepened the row at Holyrood by demanding a wider investigation into Mr Salmond's conduct than one under the terms of the ministerial code, which is already under way.
"This isn't about his future, it is about the future of Scotland, and Scotland deserves better," she said.
"That is why today I am calling for a judicial inquiry into the First Minister's handling of this affair from the beginning. An inquiry into the basis on which the First Minister did ever assert Scotland would automatically be a member of the EU.
"What made him say that this separate Scotland would not have to adopt the euro? An inquiry into why he said he'd sought advice from law officers when he had not. No amount of bluff and bluster will stop us seeking the truth."
The First Minister was not in the chamber today because he was taking part in other ministerial engagements, including an appearance at a renewable energy conference.
The SNP insists that Scotland will automatically be accepted into the EU, while opponents say it would have to reapply and lose the UK's existing rights and opt-outs.
There is no precedent in the EU for what would happen if part of a member state left to form a new independent country, and no definitive legal position exists.
Both sides of the argument have referred to comments made by authoritative figures to back their position.
Labour MEP Catherine Stihler paved the way for the latest twist by demanding to know whether the Scottish Government had taken specific advice and what that advice is.
The Government refused but was ordered by Information Commissioner Rosemary Agnew to say whether advice existed.
The Scottish Government went to the Court of Session arguing that the code of conduct for ministers prevents disclosure.
But Ms Sturgeon then revealed no advice was taken and that the legal challenge was being dropped, prompting anger from the SNP's opponents and a demand to repay taxpayers' cash.
Ms Lamont, opening a debate on the controversy in the Scottish Parliament, said that no satisfactory answers have been supplied.
"The only thing that is clear about this sorry mess is that the people of Scotland cannot expect the First Minister to be honest with them when it comes to fulfilling his lifelong dream of breaking up the United Kingdom," she said.
"The people of Scotland can no longer trust the First Minister to tell them the truth."
People deserve to know the consequences of leaving the Union, she said.
Issues include the SNP plan to continue using the pound rather than adopting the euro as a condition of potential re-entry to the EU.
"He starts with the answers he wants and then works backwards from there, whatever the truth," she said.
John Mason, an SNP backbencher, appeared to undermine the First Minister's position on automatic EU entry during the debate. He told MSPs that a definitive answer does not exist and that issues will be subject to negotiation after the referendum.
"We are not in definitive territory here. We're not really in legal territory here," he said, to applause from the Labour benches.
Green party co-convener Patrick Harvie, who supports independence, said responsibility also falls on Labour to stop demanding guarantees. Areas of doubt exist on both sides of the debate, he told Parliament.
Referring to Ms Lamont, he asked: "The Labour party as well as the SNP are responsible for the tone of this debate. Can she guarantee that if Alex Salmond and the SNP stop pretending to have cast-iron guarantees, she'll stop demanding cast-iron guarantees on issues which are subject to negotiation after the vote?"
Ms Lamont said politicians owe it to people to scrutinise the proposition for independence.
"All the evidence thus far, from the First Minister and the deputy, is they simply think assertion is enough. That is demeaning this debate and it is demeaning this Parliament and is denying the people of this country the opportunity that they require," she said.
"I do make that commitment because, precisely as I've said, in two years the people of Scotland will come together to decide our future. It will be a historic moment and our fellow citizens deserve to know exactly what they're going to vote for.
"Trust is key to this debate because the day after the referendum, we will need to come together to unite behind that result."
The ill-tempered debate began with a warning from Holyrood's Presiding Officer, Tricia Marwick. A great deal of interest is being shown in the work of the Parliament from within Scotland and beyond, she said.
"It is therefore important that we set the correct tone in our debates and in our other parliamentary engagements," she told the chamber.
"While we will not seek to inhibit debate and the legitimate holding of government to account, I remind all members in this chamber to consider very carefully their choice of words and the tone in which they have been delivered."
Ms Sturgeon said it is the Scottish Government's view that Scotland will continue in the EU, supported by "a range of opinion".
Minister's took the Information Commissioner to court based on their "interpretation" of freedom of information (FoI) law, she said, suggesting that the commissioner's "differing interpretation" would have to be resolved in the future.
Opposition leaders said ministers' "assertions" have proven to be questionable, and last week's developments made it clear that they are not based on specific legal advice.
Conservative leader Ruth Davidson called on ministers to confirm press reports that "Scotland's law officers have consistently told Alex Salmond's Government that an independent Scotland's future inside the EU was not automatic".
She also criticised Lord Advocate Frank Mulholland's rejection of her invitation to appear before parliament to clear the matter up.
Ms Sturgeon, who has frequently insisted that the "cast-iron" position is that Scotland would keep the pound, told Parliament that Scotland would not have to join the euro because "Sweden is in the EU but it doesn't use the euro because Sweden have decided not to".
There is "no contradiction between the statements of the First Minister and I last week", in which Mr Salmond said ministers have sought advice from law officers and Ms Sturgeon said they have not.
"The Scottish Government has published a number of papers on constitutional matters since 2007. These documents set out our view that an independent Scotland would continue in membership of the EU," she said.
"We have consistently quoted the views of a number of eminent legal authorities that support that position.
"We have also been clear that negotiations will be required on the terms of Scottish membership of the EU. These documents were underpinned by law officers' advice."
These publications have consistently said that "in our view" an independent Scotland would continue in the EU, she said.
"We set out a range of opinions that support that position."
Ms Sturgeon also maintained that "ministers don't confirm the fact or content of legal advice of law officers".
She said: "It is a convention that is well established and followed by successive governments. It is also enshrined in the ministerial codes for both the Scottish and UK governments. UK and Scottish FoI legislation also provide mechanisms which are used to protect legal advice both from law officers and others.
"It was in the interests of upholding our interpretation of the relevant provisions of the FoI Act that we made the decision to appeal the ruling of the Information Commissioner. That was, I believe, entirely appropriate at that time.
"We remain of the view that the protection provided in the legislation is important, and the differing interpretations of the law on the part of the Government and the commissioner will require to be resolved at a later stage."
Miss Davidson said: "We have seen ministers of this Government assert and assert and assert as fact things where the answer is unknown. They don't know whether Scots will be spending pounds or euros. They don't know whether farmers would continue getting European support. They don't know whether the Schengen agreement would alter our border controls.
"This Deputy First Minister told this chamber on Tuesday that they have not asked for law officers' advice, despite the First Minister claiming on television that advice has been sought and despite countless experts, two European Commission (EC) chairmen and the Spanish foreign minister on record saying that the opposite is true."
Miss Davidson quoted EC vice-president and Commissioner for Justice Viviane Reding who told a Spanish newspaper that Catalonia "would be considered a new state" if it separates from Spain.
"We can assume, as with Catalonia, so will Scotland," Miss Davidson said.
"When legal sources close to the First Minister are telling the national press that Scotland's law officers have consistently told Alex Salmond's Government that an independent Scotland's future inside the EU was not automatic and would require detailed negotiations, we need to know if that's true.
"Of course, the person who could clear that up is the Lord Advocate, Frank Mulholland, who wrote to me today to tell me that he has no intention of appearing before parliament to answer legitimate questions and to clarify this issue."