Labour MPs lined up to criticise Mr Corbyn at a meeting of the Parliamentary Labour Party (PLP) on Monday night that was described by those inside as “miserable”.
Following the heavy losses Labour sustained at the election, Mr Blair has warned that the party faces an existential crisis.
Mr Blair, the only Labour leader to have won a general election in the last 45 years, used a speech today to urge against a "whitewash" of the party's worst general election result since 1935.
Mr Corbyn apologised to MPs at Monday night’s meeting and assured MPs he was only staying on until a new leader is elected to ensure "the smoothest possible transition".
But a series of MPs criticised Mr Corbyn during the meeting, which veteran critic Dame Margaret Hodge described as "on the whole it was fury, despair, miserable”.
Former shadow work and pensions shadow Rachel Reeves said she told the meeting Labour needs "radical change" and to get a leader "that actually wants to win”.
Labour's Lord Falconer, a former justice secretary, told BBC's Newsnight: "The feeling is like a volcano of molten anger that is absolutely pouring out. It's been there in the building the whole day.”
Numerous Labour MPs said, however, that Mr Corbyn was not told to go immediately, with them apparently supporting his plan to depart after overseeing a "process of reflection”.
A new leader is expected to be in place by the end of March.
Mr Blair told an audience in central London that Labour faces being "replaced" if the party does not revitalise itself as a "serious, progressive" alternative to the Tories.
The ex PM, whose former seat Sedgefield fell to the Tories in Thursday's election, warned that "any attempt to whitewash this defeat, pretend it is something other than it is, or the consequence of something other than the obvious, will cause irreparable damage to our relationship with the electorate”.
Mr Blair put Mr Corbyn on notice that his planned "process of reflection" before standing down as leader will cause "irreparable damage" if it buries the reasons for the party's worst result since 1935.
However, a Labour source defended Mr Corbyn and blamed Mr Blair for having overseen the start of the party's decline.
Mr Corbyn has maintained his position that Brexit was a major reason voters lost their trust in Labour.
And with Boris Johnson’s Brexit deal coming back for a vote in Parliament this week, Mr Corbyn told his MPs to vote against it because it imposes an "impossible timetable" to get a "good" trade deal with the EU by the end of the transition period.
But the Withdrawal Agreement Bill to implement Brexit is almost certain to pass following the Tories' emphatic victory.
Potential Labour leadership candidate Sir Keir Starmer has been partly blamed for the dire election performance, in which it lost dozens of seats in Brexit-backing areas.