After his comments, the Better Together campaign said Mr Blair was a big political player and it would be willing to discuss his participation in the run-up to the 2014 referendum.
However, the SNP said his intervention was an "early Christmas present" for the Yes campaign.
The ex-premier, speaking at a lunch hosted by Westminster journalists, denied devolution had been the "spur to independence" but stressed that if devolution had not happened the battle over Scottish independence would have come earlier.
He said: "Devolution is a sensible way of keeping all the strengths of the United Kingdom while allowing decisions that really should be taken close to the people to be taken close to the people."
"If we had not done it, we would have had huge pressure for change building up in Scotland.
"There was always going to be a period of time when the Nationalists came forward.
"We're going to have to take their argument on and beat them. I think we can."
Asked if he would play a role in the pro-UK campaign, he replied: "I'm very happy to play a part in it but it's up to those who are going to organise the campaign."
In contrast, the SNP said it believed any involvement by Mr Blair in the pro-UK campaign would backfire.
Kenneth Gibson, the SNP MSP, said: "Tony Blair's cack-handed intervention at Westminster is an early Christmas present for the Yes campaign."
He likened any intervention by the former PM to Margaret Thatcher's visit to Scotland in the final stages of the 1997 devolution referendum campaign.
In a rare appearance before the media, Mr Blair defended his record on immigration, warned about scapegoating immigrants and insisted talk of leaving the EU was dangerous.
Last week, Ed Miliband said Labour "made mistakes" on immigration, including failing to impose transitional controls on migrants from new EU member states in Eastern Europe.
However, the former Prime Minister defended his record.
He said: "You can have a debate about it but, personally, I think the Polish community contributes a lot to this country.
"In many ways immigrants do a lot for our country. They bring fresh energy, fresh initiative and it will be a sad day if we end up targeting them."
Mr Blair insisted immigration was a key issue from the US to Europe, that it had to be controlled and that illegal immigration had to be tackled head on.
On Europe, the ex-premier said: "Talk of leaving is dangerous and immensely damaging to Britain's long-term interests.
"The UK has an opportunity to play a part in shaping the new Europe and it should seize it."
Despite his party voting with Tory rebels over the EU budget, Mr Blair said he was "totally confident that Labour will remain a party that wants sensible pro-European engagement".
He lashed out at the UK Independence Party, which the former PM said was "never far from being nasty and never close to being sensible". Mr Blair said UKIP "will garner a lot of protest votes but they are a party built on scapegoating not solutions."