World leaders must apply "maximum pressure" to bring about a UN resolution for a sustainable ceasefire in the Middle East, the PM has said.
Tony Blair was speaking during an official visit to San Francisco
Downing Street says Tony Blair is working "hell for leather" to find a resolution acceptable to both sides.
His comments came during a visit to San Francisco after intensive telephone talks with US President George W Bush and German Chancellor Angela Merkel.
It comes after an Israeli air strike killed more than 50 in south Lebanon.
Referring to a UN statement saying it was "shocked" by Sunday's attack on Qana, Mr Blair said: "You know the position of Israel, now there's a statement from the UN Security Council which shows the right degree of unity in the international community."
Mr Blair continued: "What's important now is that we have a real chance of getting a UN Security Council resolution, which will give us an opportunity both to have a complete cessation of hostilities and to do so on a sustainable and lasting basis."
Achieving a resolution would take "a lot of work", he said.
It must ensure security for Israel as well as "the taking back, by the Lebanese government, of full control of their country".
"Everyone is going to have to exercise the maximum restraint and maximum pressure and will to get the UN Security Council resolution agreed," he added.
"There is a chance, there is a will and I think the elements of this package can be agreed as quickly as we can and get the situation forward towards where we can see an end to the hostilities."
Downing Street says Mr Blair has already spoken on Monday to Israeli Prime Minister Ehud Olmert and Lebanese Prime Minister Fouad Siniora.
"We are working flat out in London and the UN and the US to get this UN deal done," said the prime minister's official spokesman.
Asked if that meant giving either side a veto, he replied: "We are dealing with sovereign governments, we are not dealing with puppets on a string."
The UN statement expressed "extreme shock and distress" at the deaths in Qana but did not call for an immediate ceasefire, despite an earlier appeal by Secretary General Kofi Annan.
UK Foreign Secretary Margaret Beckett said the deaths in Qana were "utterly appalling".
But she declined to comment on whether she agreed with her predecessor Jack Straw, who described Israel's military action as "disproportionate".
Instead she urged caution about the use of certain language, adding that if Israel felt people did not understand their problem "they would stop listening... we cannot afford for Israel to stop listening".
"We are trying to work for a ceasefire, just as everybody wants," she said. "But we want it to be a ceasefire that holds together for longer than a day and a half."
Paddy Tipping MP, Mr Straw's parliamentary private secretary, told the World at One the former foreign secretary's views reflected those of the Labour Party and the rest of the country.
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.