Israel launched an expanded ground offensive in Lebanon tonight as ministers scrambled to agree the text of a United Nations Security Council resolution designed to end a month of bloodshed.

News of the armoured push into southern Lebanon came from the office of Ehud Olmert, the Israeli Prime Minister, after he gave his formal approval to the offensive. Israeli television showing columns of Israeli tanks preparing to move further into Lebanon towards the Litani river that Israel wants to see as the border of an eventual buffer zone.

Israel has so far steered clear of an all-out ground war but Mr Olmert and his Government are under fire from hardliners for failing to achieve a clear-cut military victory over Hezbollah guerrillas.

Opinion polls published today showed that few Israelis are satisfied with his performance, even though an overwhelming majority still backs his decision to launch the offensive after a Hezbollah raid on July 12 in which two Israeli soldiers were abducted. Since then more than 1,000 Lebanese and 100 Israelis have been killed.

"We said two days ago that we would stop the fire, either militarily or diplomatically," an Israeli political source said. "We see that the ceasefire deal in the UN is not making the required progress, and therefore we have authorised the military action."

Mr Olmert and his defence minister, Amir Peretz, met today for four hours and chose to implement the Cabinet decision, made on Wednesday, granting the army permission to sweep to the Litani River, 13 miles (20 km) from the Israeli border.

Israel’s UN ambassador, Dan Gillerman, said Israel was still engaged in negotiations over a UN resolution despite Mr Olmert’s order. "The Americans are aware of what we can accept and cannot accept. And I very much hope that at the end of the day there will not be submitted a draft that is unacceptable to us," he said.

Joining the negotiations in New York was Margaret Beckett, the Foreign Secretary, who yesterday broke from a holiday in France. Condoleezza Rice, the United States Secretary of State, and Philippe Douste-Blazy, the French Foreign Minister - who are joint co-sponsors of the draft resolution - also arrived in New York tonight.

Israel’s apparent frustration at the slow diplomatic progress was at odds with statements from other powers, including its ally Washington. "We are now very, very close to agreement and our aspiration to have a vote at the end of the afternoon remains," John Bolton, the US ambassador to the UN, told reporters. Emyr Jones Parry, the British ambassador, backed that view.

It was unclear to what extent the stepped-up Israeli action was being used a negotiating tool or whether Mr Olmert had decided that a ceasefire would be premature if Israel's primary military objectives - including the neutralisation of Hezbollah as a threat to northern Israel - have not been achieved.

A source close to the Israeli Government said tonight that Mr Olmert had received a call from Dr Rice asking if there was still any room for diplomacy, the Associated Press reported. According to the AP report, Mr Olmert said that he would be willing to call off the offensive if his diplomatic demands were met.

Mr Olmert received an unambiguous warning today that accepting a UN-brokered ceasefire before achieving a clear-cut military victory over the Shia Muslim movement would amount to a humiliating defeat for Israel that could force him from office.

After enjoying four weeks of unwavering public support, Mr Olmert and his Government woke up to an unprecedented barrage of criticism today for its handling of the war. A headline in the Haaretz newspaper declared: "Olmert must go".

One newspaper reported a series of acrimonious exchanges between Mr Olmert and his deputy, the veteran Shimon Peres. The Maariv daily said that the two clashed notably during Wednesday's Security Cabinet meeting when ministers approved a wider ground war.

"Peres criticised the management of the crisis, the lack of thought, the fact that everyone blabs to the media and informs Hezbollah when there will be an operation," Maariv said.

A Haaretz newspaper poll found only 48 per cent satisfied with Mr Olmert's performance - down from 75 per cent. Just 20 per cent of those polled believe that that Israel is winning the campaign, against 30 per cent who say it is losing.

The Haaretz commentator Ari Shavit wrote: "One thing should be clear: if Olmert runs away now from the war he initiated, he will not be able to remain Prime Minister for even one more day.

"Chutzpah has its limits. You cannot lead an entire nation to war promising victory, produce humiliating defeat and remain in power."

In Lebanon itself, Israeli airstrikes pounded south Beirut and border crossings to Syria, killing at least 14 people across the country as ground fighting picked up intensity in the south.

Jets struck twice at a busy bridge at the Abboudiyeh border crossing into Syria, killing at least 12 people and wounding 18 others, hospital and security officials said.

At least 20 explosions rang out across the Lebanese capital as thick black smoke rose from the southern suburbs, prompting Hezbollah to fire a barrage of rockets at towns in northern Israel.

The Shia Muslim guerrilla group said that it fighters had killed or wounded about 15 Israeli soldiers trying to advance toward the border village of Aita al-Shaab, one of several hotspots where gunbattles have been raging for weeks.

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