Ex-PM Tony Blair says he still believes that ID cards are the only way of dealing with illegal immigration.
Mr Blair said it was "fair in some ways" for Labour leader Ed Miliband to say he had got things wrong on immigration.
But he said the "central problem is not about immigration per se... it's where it uncontrolled, it's illegal and there's organised crime and drugs".
ID cards were "out of fashion" but were the only way of dealing with that.
On Friday Mr Miliband said that Labour had made a mistake in allowing unlimited access to work in the UK when the first wave of eastern European countries joined the EU.
Asked about the criticism, Mr Blair said: "I think it's fair in some ways - I actually took the decision. But in some ways I don't regret it actually because I think the Polish community and other communities from eastern Europe do good work in our country.
"I'm happy with them, but I understand there's a marked sensitivity about that."
In his speech Mr Miliband also said: "By focusing exclusively on immigration's impact on growth, we lost sight of who was benefiting from that growth - whose living standards were being squeezed. We became disconnected from the concerns of working people."
He said Labour had told people concerned about the biggest peacetime migration to the UK to "like it or lump it" and that the public had been "ahead of us" on the issue.
Mr Blair, who was prime minister from 1997 to 2007, told the BBC's Andrew Marr Show that he had fought the 2005 election on immigration after then Conservative leader Michael Howard "wanted to make that a point of attack against us".
But, he said: "We confronted it and took it head-on because we had a policy at the time, identity cards, which have gone out of fashion but I still think are the only way of dealing with what is the central problem here.
"It's not so much about immigration per se. Most reasonable people in Britain can see that immigrants have made a great contribution to our country.
"It's where it's uncontrolled, it's illegal, where people come in and you've got organised crime and drugs and so on."
He said that these problems came from very specific places, adding that "in my view, you can get to a balanced debate on this and that's what Ed's trying to do".
The issue of identity cards was a long-running cause of controversy for the last Labour government from 2002 when the plans for a national ID card were set out.
Both the Conservatives and Lib Dems pledged to scrap the scheme if elected in 2010, and after they formed their coalition government the ID card scheme was axed within 100 days.
Asked more broadly about Labour's prospects, five years after he stepped down as leader and prime minister, Mr Blair said he had been impressed by Mr Miliband, and the good news was that they had not gone "crazy" like they had in 1979.
"We're going to be in contention at the next election and that's a tribute to the leadership" and a sign that the party was "a lot more mature and smarter today", he said.