The former prime minister confirmed he is in touch with the Independent Group, although he said he did not speak to those MPs about leaving Labour and the Conservatives to establish it.
Mr Blair also said he is “deeply concerned” about Labour’s direction and policy under Jeremy Corbyn’s leadership, adding this would not help the party “get back to winning ways”.
He claimed the combination of a “hard-left” Labour and “hard Brexit” Conservative Party will allow others to cultivate “fertile” political territory.
The Independent Group is formed of eight ex-Labour MPs and three ex-Tory MPs who have adopted a centrist outlook in a bid to change the debate on Brexit and other issues.
Asked if he spoke to any of the MPs who broke away to form the group, Mr Blair told BBC One’s Andrew Marr Show: “I didn’t. I’ve spoken to them many, many times but speaking about breaking away? No.”
Pressed about whether he has been in contact since, he said: “I’m in touch with them and I have spoken to some of them.
“I’ve got a great deal of sympathy with what they’re doing and what they’re saying.”
Mr Blair went on: “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.
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“But do I sympathise with what they have done? Yes, I do. I think they’re courageous in having done it.”
Mr Blair added: “I think it’s absolutely inevitable that if you put the choice before the country - hard Brexit Tory party, hard-left Labour Party - it doesn’t matter what I say, what I want to happen, what anyone else says, you leave that amount of fertile territory open, someone is going to cultivate it.”
Mr Blair expressed concerns about Labour’s current position, before saying: “If you want to get back to winning ways, this is not the position to be in.”
He said he believed Labour deputy leader Tom Watson has “shown really great leadership” in recent weeks when asked about the move to set up a social democratic group within the party.
Mr Blair added: “As a result of what he’s doing, he’s encouraging people who do share a perspective of the Labour Party as a governing, modern, progressive party, he’s actually encouraging them in a sense to stay because he’s providing a space within which people can debate and argue.”
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.
“We’re a pluralist broad church and let’s welcome that.”
Labour peer Lord Falconer of Thoroton, who served as a minister under Mr Blair, said he is “not at all” tempted to leave the party.
But he told BBC Radio 5 Live’s Pienaar’s Politics: “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.”