The leaders reaffirmed commitment to the 'road map' for peace
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The UK Government has rejected Israeli Prime Minister Ariel Sharon's appeals for Britain to break off relations with Palestinian leader Yasser Arafat.
Mr Sharon wants European leaders to cut ties with Mr Arafat, who he says is interfering in the work of Mahmoud Abbas, the moderate Palestinian prime minister.
But that suggestion was rebuffed during talks with UK Foreign Secretary Jack Straw in London.
Later Mr Sharon and Tony Blair reaffirmed their commitment to the internationally-backed "road map" to peace in the Middle East during discussions over dinner in Downing Street on Monday.
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It was a very warm and constructive private dinner lasting around two and a half hours
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"It was a very warm and constructive private dinner lasting around two and a half hours," a Downing Street spokesman said.
"The focus was on the Middle East peace process. Both sides restated their commitment to the success of the road map and undertook to continue to work closely together to advance it.
"They also discussed a range of regional and bilateral issues."
The meeting came amid a noisy demonstration by several hundred pro-Palestinian protesters.
Shootings
After Mr Sharon's meeting with Mr Straw, British officials said Mr Arafat was an elected leader and the UK would continue to deal with him where it was appropriate.
The foreign secretary used the talks to raise the question of the shooting of three British citizens by the Israeli army in the occupied territories in recent months.
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It is a major mistake to keep up contact with Arafat, because he is undermining Abu Mazen's government
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In response, Mr Sharon said he had given instructions for the incidents to be investigated.
The Israeli leader is due to meet with Tory leader Iain Duncan Smith at the end of his two-day trip to London.
His visit is being seen as an attempt to ease strained Israeli-UK relations and to push forward the Middle East peace process.
Political violence
Ties between the UK and Israel were strained when Britain hosted a conference on Palestinian reform in January and Israel prevented Palestinian delegates from travelling to the meeting.
Tensions have also risen over a suicide bomb attack in Tel Aviv in April which was blamed on two British Muslims.
Mr Blair is keen to see progress on the US-backed roadmap for peace which would see a Palestinian state set up by 2005.
While Mr Sharon was in London, a Palestinian man stabbed three people in Tel Aviv, in what police describe as the first case of political violence in an Israeli city since Palestinian groups declared a truce in June.
One of the victims later died in hospital.
The attacker was shot in the leg and restrained by security guards from a nearby restaurant until police arrived.
On Monday evening, Mahmoud Abbas said he had settled his differences with Yasser Arafat at talks at the Palestinian leader's headquarters in Ramallah.