Downing Street rebuffed Foreign Office (FCO) calls for the prime minister to argue for an end to hostilities in the Middle East, BBC News has learned.
Mrs Beckett's department urged pressure for a ceasefire
A ministerial source says FCO officials tried "strenuously" to get him to press the case during his US visit.
BBC political correspondent James Hardy said the exchange took place last week.
He also said more than the three known Cabinet "doubters" had signalled to Mr Blair their unease over the failure to call for an immediate ceasefire.
It has been widely reported that at last Thursday's Cabinet meeting Environment Secretary David Miliband raised concerns about the UK's position.
Commons leader and ex-Foreign Secretary Jack Straw and International Development Secretary Hilary Benn have also raised public concerns.
But the BBC has learned that one or more other ministers passed notes to Mr Blair at the Cabinet meeting "saying that he should not take their silence as consent for this policy".
It is thought Foreign Office officials would have made the request on behalf of Foreign Secretary Margaret Beckett.
She is known to have been deeply concerned that America and Britain appeared to be giving the Israelis "a green light" to continue bombing.
Mrs Beckett and Mr Blair have both said that the UK wants an end to the violence that lasts, rather than calling for an immediate ceasefire which they say they fear might not.
They say such a move must ensure security for Israel as well as "the taking back, by the Lebanese government, of full control of their country".
Ex-minister Michael Meacher said there was "despair, anger and bewilderment" in the Labour Party at the UK's failure thus far to call for an immediate ceasefire.
Aid campaigners, who delivered a petition signed by more than 35,000 to Downing Street, also criticised Mr Blair for not doing enough to exert pressure on US President George Bush.
Joined by ex-MP and war reporter Martin Bell and Muhammad Abdul Bari, secretary general of the Muslim Council of Britain, the group called for an immediate ceasefire to allow urgent aid to reach those in need.
Dr Bari said Mr Blair was "the one world politician people think has influence on America and he must try his best to get a ceasefire".
"How can talks go ahead while bombing is going on?" he asked.
In a speech to the World Affairs Council in Los Angeles, Mr Blair will call for nations worldwide to have a radical rethink of foreign policy in the wake of the Israel-Lebanon crisis.
He told the 2,000-strong audience the forces of moderate Islam must prevail over reactionary and terrorist elements.
"We will not win the battle against this global extremism unless we win it at the level of values as much as force, unless we show we are even handed, fair and just in our application of those values to the world," he said.
And he admitted: "In reality we are at present far away from persuading those we need to persuade that this is true."
Meanwhile, Mrs Beckett and other EU foreign ministers in Brussels agreed a draft proposal calling for an "immediate cessation of hostilities", to be followed by a sustainable ceasefire.
The original text called directly for an immediate ceasefire but it is understood it was watered down in the face of British, German, Polish and Czech pressure.
The Foreign Office is refusing to comment on reports that Mrs Beckett is postponing her caravan holiday while the crisis continues.
A spokesman said: "She is remaining engaged on this. She will go on holiday when she decides the time is right."