Senior ministers have spoken out in support of the prime minister after suggestions of a Cabinet split over the Middle East crisis.
They rallied around after Commons leader Jack Straw criticised Israel's "disproportionate" attacks on Lebanon.
Downing Street said Tony Blair would not endorse or criticise the remarks.
Foreign Secretary Margaret Beckett and Lord Chancellor Lord Falconer have both backed the prime minister and dismissed reports of a split.
In his statement, Mr Straw - foreign secretary before May's reshuffle - warned that a continuation of Israeli military action in Lebanon "could further destabilise the already fragile Lebanese nation".
Mr Straw backed Foreign Office Minister Kim Howells' description of Israeli action as "disproportionate".
Mr Blair has come under pressure from within his own party for not calling for an immediate ceasefire in southern Lebanon. He said that was not the solution to the crisis.
He wants the UN to agree a resolution with both Israel and Hezbollah to end the fighting, and send an international force of peacekeepers to southern Lebanon.
Speaking on Sunday, Lord Falconer insisted there had been a "non-divisive discussion" about the way forward in the crisis at Thursday's Cabinet meeting.
The UN has called for a three-day truce between Israel and Hezbollah
"We are all as supportive as we can be of trying to bring the thing to an end," he told the BBC's News 24 Sunday programme.
"I've read what Jack says and Jack gives a balanced account of what's going on and he says, like all of us, we're looking for a durable ceasefire that has some prospect of lasting."
And Mrs Beckett - who called Sunday's Israeli strike on Lebanon in which at least 34 children died "appalling" - told Sky News the Cabinet was not divided over the issue of a ceasefire.
"There's not a single person in the Cabinet who is not desperately anxious about the situation...and agonising over whether we are in fact doing everything we can," she said.
"Everyone is united on that point of view round the Cabinet table as they are in the international community right around the world."
But Lib Dem leader Menzies Campbell, who said the worsening crisis in the Middle East was "deeply depressing", suggested there was a Cabinet split over what action to take.
"What Jack Straw has had to say suggests, shall we put it this way, a difference of emphasis [within the Cabinet]."
Mr Blair has maintained that, for any truce to work both Israel and Hezbollah had to be engaged in it.
"It cannot be that Israel stops taking the action it's taking but Hezbollah continue to kill, kidnap, and launch rockets into the north of Israel at the civilian population there," he told BBC political editor Nick Robinson.
Mr Blair said if an agreement could be "endorsed by the governments of Israel and Lebanon" and could be "encapsulated in a UN resolution", the conflict could be stopped.
He added this "could happen in days if the international community is willing to act with the urgency I want it to act with".
The prime minister, who held talks with President Bush at the White House on Friday, is now spending several days in California promoting his climate change plans and UK hi-tech business.
The Israeli assault began after Hezbollah captured two Israeli soldiers and killed eight in a cross-border raid on 12 July.
Some 750 Lebanese, the majority civilians, have been confirmed killed in the conflict. Fifty-one Israelis, including at least 18 civilians, have been killed, mostly by Hezbollah rockets.
Shadow defence secretary Liam Fox criticised Hezbollah for "putting rocket launchers in people's back gardens" but said the number of Lebanese civilians killed in the conflict was not proportionate.
The rest of the world had not done enough to help maintain peace since the withdrawal of Israeli troops from Lebanon six years ago, he told News 24 Sunday.
"And now, of course, when it comes to the sort of dreadful violence involving mass civilian killings which we've seen then we're all standing up and taking the moral high ground."