Tony Blair says he is staying in the Labour Party despite having a "great deal of sympathy" with breakaway MPs.
The former Labour leader said he had not spoken to the MPs before they quit the party but he had been in touch with "some of them" since.
"Hard-left" Labour and a "hard Brexit" Tory party had created a "vast" new space, he told the BBC's Andrew Marr.
Eight MPs quit Labour and joined forces with three former Tories to form a new Independent Group in Parliament.
The eight are all longstanding critics of Labour leader Jeremy Corbyn. They all support the People's Vote campaign for another EU referendum - and have been highly critical of Labour's response to anti-Semitism allegations.
They have not yet formed a new party and have no plans at this stage to fight elections, but they say they want to provide an alternative to the "broken" two party system.
Mr Blair said: "I've got a great deal of sympathy with what they're doing and what they're saying."
But he added: "I'm staying in the Labour Party. I've been in the Labour Party for over 40 years, I led it for 13 years, I was the longest-serving Labour prime minister, I'm deeply attached to the Labour Party.
"But do I sympathise with what they have done? Yes, I do. I think they're courageous in having done it."
He said the move showed there was "a limit to the self-indulgence" of the two main parties, as they moved further to the left and right, respectively, leaving millions of voters politically "homeless".
And he warned: "You are going to have a situation in which the two main parties break up."
Mr Blair's name has been linked to the formation of a new centre ground party for some time, but he has never publicly confirmed it.
He said he believed Labour's Deputy Leader Tom Watson had "shown really great leadership" in recent weeks by setting up a forum for centrist Labour MPs.
"He's actually encouraging them, in a sense, to stay because he's providing a space within which people can debate and argue," said Mr Blair.
Earlier, shadow chancellor John McDonnell pointed to different groups which already exist within Labour.
He told Sky News' Sophy Ridge on Sunday: "Tom is bringing other people together, he has a perfect right to do that, that's fair enough.
"We need as much policy debate as we possibly can and I welcome that."
Lord Falconer, a close ally of Mr Blair during his years in government, has also ruled out joining the new Independent Group, but he said some colleagues in the House of Lords were clearly "toying" with quitting the party.
"I am completely committed to Labour. I am too old to leave," the former Lord Chancellor told BBC Radio 5 Live's Pienaar's Politics.
But he added: "There's a lot of anxiety in the Lords about the leadership of the Labour Party and there are a lot of people, I suspect, toying with whether they're staying or not."
The former justice secretary is leading a review into cases of anti-Semitism in the Labour Party.
The Independent Group of MPs appointed former Labour MP Chuka Umunna as its spokesman on Friday, and announced who would be speaking in different policy areas.