Foreign Office minister Kim Howells has begun talks with Israeli officials a day after criticising the country's military tactics in Lebanon.
Rallies have been held in the UK
He met the mayor of Haifa and is expected to meet Israel's Foreign Minister, Tzipi Livni, in Jerusalem.
US Secretary of State Condoleezza Rice arrives in the region later on Monday.
In the UK a rally showing solidarity with people in northern Israel - areas of which have been hit by Hezbollah rockets - was held on Sunday.
It was organised by the Board of Deputies of British Jews and comes a day after 11 rallies across the UK in protest against Israel's actions.
Israel's ambassador to the UK, Zvi Heifetz, told the event in Kenton, north-west London Israel had "the right to defend its people".
Organisers said about 7,500 people attended the event but a police officer put the figure at between 4,000 and 5,000.
Mr Howells, the first government minister to condemn the Israeli action, is also expected to meet Palestinian president Mahmoud Abbas during his tour.
He told the BBC that during meetings with Israeli officials he had repeated his criticisms that too many civilians were dying as Israel's military tried to wipe out Hezbollah.
But they had replied: "What other way have we got of doing it?", he said.
Mr Howells said Hezbollah must be defeated by political and diplomatic means but calling for a ceasefire was not enough.
"The Russians, the Chinese, the Saudis, the Egyptians - they've all got to condemn what's going on as well as Britain and the United States," he said.
While visiting Beirut on Saturday, the minister had said the deaths of "so many children" in Lebanon meant the strikes had not been surgical.
"It's very difficult, I think, to understand the kind of military tactics that have been used. You know, if they're chasing Hezbollah, then go for Hezbollah. You don't go for the entire Lebanese nation."
'Yes to peace'
Downing Street said the prime minister would stand by the comments Mr Howells made on Saturday, adding the British government had "always urged restraint on Israel".
Jon Benjamin, chief executive of the Board of Deputies of British Jews, said there was great concern about the casualties and fatalities on all sides.
He said: "There are a million Israelis... spending their days and nights in bomb shelters under direct attack from people focussed on killing as many civilians as possible."
Kim Howells says the government is "trying to make peace work"
Liberal Democrat leader Sir Menzies Campbell said he welcomed Mr Howells' comments but he criticised the way ministers had refused to call for a ceasefire.
"I simply cannot believe a Labour government finding itself at odds with the Secretary General of the United Nations, calling for a ceasefire in these circumstances," he said.
It is thought Israel wants to set up a deep buffer zone in southern Lebanon to try to stop Hezbollah from using the area to launch rocket attacks.
Israel launched strikes against Lebanon following the capture of two Israeli soldiers by Hezbollah militants, who responded with rocket fire.
About 4,400 people have been taken out of Lebanon by the British; in total about 25,000 foreign nationals have been evacuated.