Up to 100 MPs - most of them Labour and a number of ex-ministers - are demanding a recall of Parliament to debate the crisis in the Middle East.
The prime minister is currently away in the Caribbean
A letter arguing that MPs need to be able to discuss the government's strategy is expected to be delivered to Commons leader Jack Straw on Wednesday.
Any recall decision would be a matter for the Speaker, Michael Martin, based on the advice given by ministers.
Downing Street refused to comment in advance of any letter being delivered.
A No 10 spokeswoman said it was "a matter for the leader of the Commons".
Jon Trickett, chairman of the 50-strong Compass group of left-wing Labour MPs, has organised the campaign, along with ex-ministers Clare Short, John Denham and Tony Lloyd.
Other signatories include: Lib Dem leader Sir Menzies Campbell, SNP leader Alex Salmond and Plaid Cymru's Elfyn Llywd.
Mr Trickett told BBC Radio 4's World at One (Wato) programme he believed a quarter of members of the House of Commons will have signed the letter before it is delivered.
"The point is that the nation is very concerned about the trouble in the Middle East - there are people dying in front of us every day," he said.
"We live in a 24/7 society and it's extraordinary that Parliament should be away for 11 weeks. I think people expect MPs to give a voice to their concerns."
Sir Menzies said if Parliament had not been in recess, the prime minister would have been expected to make a statement on the current crisis.
"Given the uncertainties and worsening situation in the Middle East, Parliament needs to be recalled as a matter of urgency," he said.
"Parliament must now have a chance to discuss the government and UN's strategy in detail. The need for an immediate ceasefire is as pressing as ever."
"Given the massive concern in the country about these matters, we believe that it is right to allow the Commons to meet in order that the government's strategy can be fully discussed," the MPs' letter says.
But Conservative peer Baroness Fookes, a former deputy speaker in the Commons, says while it is technically the Speaker who recalls Parliament, the government has the final say.
"So he can't recall Parliament purely on his own initiative," she told Wato.
She said the seniority of those asking for the Commons to return was more likely to sway ministers into making that decision than the numbers involved.
She agreed that the Middle East situation was "an emergency", but added: "I am not sure what practical use it would be if they were recalled bearing I mind we are very much secondary players in this, never mind Parliament."
Blair 'on the phone'
The demand comes amid growing concern at the government's strategy in dealing with the crisis.
But Foreign Office Minister Kim Howells said he was not sure what bringing MPs back from their recess would achieve.
"I'm sure that people feel very, very concerned about the situation in Lebanon - I certainly do," he said at a press conference with Afghanistan's counter narcotics minister.
"I'm not sure what a recall of Parliament would do to alter the situation."
Tony Blair has just begun his holiday in the Caribbean, which he had delayed to try to help push through a UN resolution on a ceasefire between Israel and Hezbollah.
Mr Howells said the prime minister was "ringing everyone who is going to bring any influence on this".
And he was frequently in touch with Foreign Secretary Margaret Beckett, who is caravanning in France with her husband, and other officials concerning the crisis, he said.
Mr Howells, who last month criticised the Israeli response as disproportionate, defended Mr Blair's refusal to call for an immediate ceasefire.
He argued that other countries who have made such a demand did not appear to be pulling their weight to achieve it.
Deputy Prime Minister John Prescott is expected to take control of the day-to-day running of the country in Mr Blair's absence from the UK.