Tony Blair's supporters have brushed off calls for him to quit, as he puts the finishing touches to his top team.
Mr Blair is facing calls for him to quit
Several former Cabinet ministers are among those urging him to stand aside in months, not years, after Labour lost 47 seats at the general election.
Clare Short said it would be best if Mr Blair went quickly, but new Work and Pensions Secretary David Blunkett called backbenchers "self-indulgent".
Mr Blair will complete his team by naming junior ministers.
On Friday, several senior posts were filled in a Cabinet reshuffle which saw the return of Mr Blunkett to government.
'Weaker and weaker'
Monday's announcements will be examined carefully for their significance over the possible future direction of the government.
The prime minister has been under growing attack since his majority was slashed from 161 to 67.
11 May: MPs sworn in
11 May: Meeting of PLP
17 May: Queen's Speech
29 May: French referendum on EU Constitution
1 July: Britain takes over EU presidency
6-8 July: Britain hosts G8 summit
25-29 Sep: Labour Party Conference
Before the election he had said he wanted to serve a full third term to carry forward public service reforms.
But former Cabinet ministers Frank Dobson and Robin Cook have joined the roll-call of MPs calling for him to stand down.
On Monday former international development secretary Clare Short told BBC Radio 4's Today programme she thought it would be best for the party if Mr Blair announced soon that he was leaving, but added: "I don't think he'll do it."
She said: "The whole story of the government is going to be: 'When is he going?'. We can't think afresh because he's still there.
"There's a real danger the government looks divided, doesn't renew itself, we lose seats in the local government elections and get weaker and weaker. I'm afraid that's the likely story."
One Labour MP, John Austin said a "stalking horse" leadership challenge may be one tactic used, if, by October, Mr Blair had not announced his intention to step down.
He said Mr Blair could go after the G8 summit at Gleneagles in July with "some considerable credit, having won three elections".
"Mr Blair's reputation can only be damaged by staying on too long," he added.
'Forward, not back'
Labour's Ian Davidson, MP for Glasgow South West, said Mr Blair should start planning his leaving date now.
"We have won three terms of a Labour Government - we have got to be immensely grateful to Tony for that - but we have got to look forward, not back," said Mr Davidson.
But Mr Blair's supporters say those calling for the prime minister to go are behaving as though Labour lost the general election.
NEW LOOK COMMONS
A record 127 MPs are women
Labour has 97, Tories 17, Lib Dems 10, Sinn Fein 1, UUP 1, DUP 1
15 ethnic minority MPs, two Tory, 13 Labour
Youngest MP is Lib Dem Jo Swinson, 25
Oldest MP is Labour's Piara Khabra who is 80
Alan Johnson, productivity, energy and industry secretary, said that the government had a majority "that most politicians would give their eye teeth for".
And new Northern Ireland Secretary Peter Hain challenged critics to make their views known to colleagues at the Parliamentary Labour Party (PLP) meeting on Wednesday rather than just "taking to the airwaves".
People wanted to see the government deliver its manifesto commitments, not "squabbling" about the leadership, he said.
Despite the reduced majority, he said many of the "radical" manifesto commitments - such as those on maternity leave and child care - would be supported by all Labour MPs.
"You will see a government with real momentum and fizz and energy coming in, starting with the Queen's Speech next week, and with measures to follow around which I think all Labour MPs can unite," he said.
New Work and Pensions Secretary David Blunkett said those saying Mr Blair should go were trying to "snatch defeat from the jaws of victory".
Former welfare reform minister Frank Field, who was sacked in 1998, said: "I think those attacks are unforgivable and I speak as somebody who in a sense owes Mr Blair nothing - after all, he screwed up my career."
He said MPs calling for Mr Blair's removal had stood on an election ticket that he would stand for four years.
"I think it treacherous to somehow tear up that agreement," he told BBC Radio 4's the World at One.
And Labour election adviser Alastair Campbell warned: "Those who write him off today are doing so very, very prematurely."
A bid to oust Mr Blair as party leader would require a challenger to have the backing of 20% of Labour MPs - 71 out of the 355 elected on Thursday.
A vote would then take place at Labour conference involving an electoral college divided into three - MPs, constituency parties and unions.