"Renewal is vital," he said, using a word that has been bandied about by Labour critics in recent weeks.
"But for me renewal starts not with looking back in anger but looking forward in hope and expectation. The hope is founded on a clear conviction: if we remain New Labour we will remain in office."
Blair, 53, has been in Downing Street for nine years, but questions over his future have persisted after he declared that he would serve no more than three terms as prime minister, ceding the Labour helm to Brown.
He removed Clarke as home secretary — the cabinet minister responsible for policing and prisons — in a sweeping reshuffle in May, amid a furore over a failure to consider more than 1,000 foreign convicts for deportation from Britain following their jail terms.
Clarke was offered other positions in cabinet, but turned them down, opting to become a backbench Labour member of parliament, free to level the kind of criticism he delivered on Tuesday.
His comments were seized on by the Conservatives, who likened them to the stinging attack in parliament from one-time cabinet minister Geoffrey Howe that precipitated the downfall of Tory prime minister Margaret Thatcher in 1990.
"It is a Blairite equivalent, a media-based equivalent, of what Geoffrey Howe did to Margaret Thatcher all those years ago," the Conservatives’ home affairs critic David Davis told the BBC.