David Cameron has signalled that he is open to going beyond the Smith Commission agreement in devolving more powers to Holyrood, but has ruled out devo max.

The Prime Minister, speaking in Edinburgh after he held talks with Nicola Sturgeon at Bute House, also suggested that he had won a mandate to scrap the Human Rights Act in Scotland, despite only one Tory MP winning a seat north of the border.

Speaking about the possibility of more powers for Holyrood beyond the Smith proposals, he said: "I don't rule out making other changes if sensible suggestions are made."

He also appeared to rule out giving in to Ms Sturgeon's demand that Scotland, Wales and Northern Ireland are granted a veto should Britain vote to leave the EU.

The Prime Minister said he believed in a "respect agenda" and had held a "very positive meeting" with the First Minister, a week after he won a majority in the general election.

He confirmed that he would deliver a Scotland Bill, delivering on the Smith proposals "in full", in his Government's first Queens Speech.

Asked about the possibility of going beyond the deal, following the SNP's stunning victory which saw the party win 56 of 59 seats in Scotland, he said: "What we agreed is let's implement Smith, and let's make sure it really is Smith, we are going to look again at welfare and make sure the clauses reflect what that agreement was.

"If the First Minister wants to send some proposals for me to look at I'm very happy to examine proposals. There's going to be a debate. I don't rule out making other changes if sensible suggestions are made.

"There's going to be a debate in Parliament. The Scottish National Party now has 56 members of Parliament. There's going to be a Scotland Bill. It will be an opportunity for them to put forward amendments. There'll be debates over that Bill. I think it will be quite good that those people who want full fiscal autonomy will have to define what they mean and put forward proposals everyone else can scrutinise."

However, he added that he backed retaining the "solidarity" of the United Kingdom. He added: "I don't support full fiscal autonomy. I put it like this: Scotland has voted to stay part of the UK, I'm delighted about that, but I think there are two potential futures. The future I would offer, and I think many others would offer, is a much stronger Scottish Parliament with these tax and spending powers, and extra powers Smith talks about, but also with the solidarity of the United Kingdom.

"I want the people of Scotland to know that all of the United Kingdom stands behind your pensions, stands behind unemployment benefit, will stand behind Scotland if it has a difficult year, if the oil price goes down.

"I think the option of full fiscal autonomy for Scotland within the United Kingdom is not a good option. I think it would land Scottish taxpayers with £7 billion of extra taxes or extra cuts... it's an honest disagreement between the First Minister and me about this. But we will deliver a stronger Scottish Parliament, be in no doubt about it."

He defended his decision to make Andrew Dunlop a peer and appoint him as a junior minister in the Scotland Office. He said he was "extremely talented" and dismissed SNP suggestions that he had been behind the poll tax.

He said that a second independence referendum, which he had signalled he would block, "was not remotely on the cards". A senior SNP source had suggested that the party could hold a referendum without UK Government approval.

On the issue of repealing the Human Rights Act, which will be opposed by the Scottish Parliament and which will potentially have to grant its consent, he the Prime Minister said: "We made a very clear manifesto promise and we have a mandate for that promise. Some people interpret this as being against human rights - it isn't. It's to have a British Bill of Rights written into UK law.

"Clearly, there are going to have to be discussions between the UK and Scottish Governments and indeed UK and Welsh Governments about how exactly to make this work. There are some great complexities here but I'm sure it's not beyond the wit of clever people to make this work."

He added that he felt he had "a mandate" for an in-out referendum on the EU, which he said was a "UK pledge".

Asked about the possibility of a veto for the UK's member nations, he said: "We put forward in a manifesto the clearest possible pledge of a renegotiation and an in-out referendum by the end of 2017. That manifesto has now been backed at a UK wide general election so I believe I have a mandate for that. Rather in the same way that the SNP felt they had a mandate for the referendum, they didn't give Orkney and Shetland an opt-out, or the Borders. So this is a UK pledge, it will be delivered for the UK, and debated and discussed in Parliament."