The prime minister came out fighting at his weekly Prime Minister's Questions in the lower House of Commons and deflected a barrage of questions on the subject from the main opposition Conservative Party and its leader, David Cameron.
Mr Cameron needled Blair over health sector job losses, the failure to deport foreign convicts upon their release from prison, and Labour's poor local election showing last week that have all fuelled calls for Mr Blair to go.
He also referred to a poll in Wednesday's Daily Telegraph that suggested Mr Blair - whose satisfaction rating was 83 percent soon after taking office in 1997 - is now the most unpopular Labour prime minister since the 1960s.
"If he sets a timetable for leaving, he has told us there will be paralysis, but if he refuses to set a timetable, his government will remain paralysed," Mr Cameron stated.
"Isn't it becoming increasingly clear that he should go, and go soon?"
Mr Blair, who has announced his intention to step down before the next general election to be held by 2010 at the latest, said he had "no intention" of debating with Mr Cameron about when he will leave.
Instead, he accused his opponent of not wanting to talk about policy.
"In the end it is policies... that ultimately will determine the fate of this government and the decision of the electorate at the next election," he added, accusing Mr Cameron's Tories of lacking in substance.
Support from Clinton
Former US President Bill Clinton sprang to the defence of his embattled old friend, insisting Britain is "way better off" thanks to Mr Blair’s leadership.
Speaking at a dinner in Glasgow, where he was asked which world leaders had most impressed him during his 1993-2001 stint in the White House, Mr Clinton recalled his close relationship with Mr Blair, who came to power in 1997.
"Whatever political problems the government is in, the United Kingdom is way better off than it would have been had it not been governed the way it has for the last 10 years," he said.
Mr Blair's performance in parliament came on the heels of his attempts to reassert his authority following one of the most difficult weeks during his nine years in office.
But the issue of his succession still dominated. Critics within his party, including former ministers, have argued this week that the matter will continue to dominate, swamping Labour's agenda, if no statement is forthcoming.
That would also affect Mr Blair's cherished aim of a "stable and orderly transition" to his successor, they argue.
The YouGov/Daily Telegraph poll suggested overall support for Mr Blair's administration is on a downslide: the Conservatives commanded 37 percent of the vote, with Labour on 31 percent and 17 for the smaller Liberal Democrats.
A separate poll for The Times put support for Labour at its lowest ebb since 1992.
Veiled references were made from the Conservative benches to the extra-marital activities of Deputy Prime Minister John Prescott, whose affair with one of his secretaries, Tracey Temple, has dominated newspapers.
Mr Prescott was stripped of many of his responsibilities in Friday's shake-up, but controversially allowed to keep his salary and tax payer-funded homes.
Mr Blair defended his loyal right-hand man against Tory broadsides, comparing his record of presiding over three straight election victories to the previous Conservative deputy prime minister Michael Heseltine's.
Mr Heseltine saw his party suffer their largest election defeat in 1997.
"I'd rather have Prezza than Hezza," Mr Blair said.
London's Metropolitan Police said Mr Prescott will not face a criminal inquiry over allegations of misconduct in public office following claims that he and Ms Temple had sex in his ministerial office during government working hours.
Deputy Assistant Commissioner John Yates said he’d not consider such a probe to be a "proportionate response or an appropriate use of police resources".