The leader of the think tank whose ideas Tony Blair says could lose Labour the next election has hit back.
Compass says Tony Blair should set out a timetable
Neal Lawson, chairman of the left-leaning group Compass, said: "I don't find extremists in the Labour Party any more.
"I don't think there is anything to be scared of in debate."
Speaking at a meeting to discuss last week's local election results, Mr Lawson said voters could soon be ready to side with David Cameron's Tories.
'Road to defeat'
Compass last week called for a timetable for Mr Blair to step aside.
That prompted Home Secretary John Reid to warn against allowing an "Old Labour lobby group" dictate the party's future.
And at his monthly news conference, Mr Blair said the policies of Compass were the "surest route to opposition".
At Wednesday evening's meeting inside Parliament, Mr Lawson said those expecting the "political equivalent of Walking with Dinosaurs" would be disappointed.
"We are an organisation packed with people who were fighting Trotskyites when some of the modernisers were Trotskyites," he said.
"We think the qualification of being a moderniser is not just that you are in the New Communist Party."
Mr Lawson said Labour had to address issues such as immigration and how to personalise public services without commercialising them.
The party had to renew itself and find the right balance between the "politics of power and the politics of purpose", he said.
It was not the time to tie leaders down and "go back to the old politics of betrayal" but the Labour crown should not be passed on without a real debate.
The think tank chief said he had heard Mr Cameron give a speech about democratic decline last weekend which, except for his views on voting reform, had been better than any current Labour politician could deliver.
"I don't think British people are ready yet to throw their lot in with Cameron, but I don't think it would be too much."
Jon Trickett, Labour MP for Hemsworth, West Yorkshire, said it was ominous that votes of people with a social conscience had gone to the Tories for the first time in a generation.
Raj Chada, who was Labour leader on Camden Council before the party lost control in the local elections, said he had not detected any mass enthusiasm for Mr Cameron.
But the previous anti-Conservative coalition had begun to break it up and so fear of voting Tory was disappearing.
"That's the challenge," said Mr Chada, who argued that telling people that voting Liberal Democrats would let in the Tories was no longer working.
Local issues had been important but national circumstances had also played their part, he said.
Turnout had been high in marginal wards, with the Labour vote itself up.
"But people actively came out and voted to give us a kicking and that is a much more dangerous issue than the idea that this is simply a mid-term political blue...
"They wanted to get rid of a Labour council, they wanted to make sure the government knew about it."
Emily Thornberry, MP for nearby Islington and Finsbury, pointed to Labour gains on Islington council.
The party's "on your side" slogans had helped and Labour had to reconnect and be "genuine".
"If people know we mean it then they do vote Labour," she said.
Other activists stressed there was not a national picture from the elections and circumstances differed from area to area and Labour had won strong support from Muslim and black voters.