Prime Minister Gordon Brown said he could see a "clear path to peace" in the Middle East in the wake of the ceasefires declared by both sides in the Gaza conflict.
Mr Brown was speaking in Jerusalem as his Israeli counterpart Ehud Olmert declared that he wants to withdraw his troops from the Palestinian territory as soon as it is clear that Hamas intends to stick to its cessation of rocket attacks on the south of the country.
Hamas, which controls the Gaza Strip, announced its own ceasefire, shortly after Israel halted its 22-day air and ground offensive, which has claimed more than 1,200 Palestinian lives.
The ceasefires came after Mr Brown, together with French President Nicolas Sarkozy and German Chancellor Angela Merkel wrote to Mr Olmert offering European help in stemming the flow of arms to Hamas by sea and through tunnels linking the enclave to Egypt.
Mr Brown confirmed that this could mean the involvement of Royal Navy ships intercepting smugglers in the Red Sea and Gulf of Aden.
The three leaders were among a group of European leaders who held talks with Mr Olmert at his Jerusalem residence after attending a hastily arranged international summit in Egypt to discuss the next steps forward in Gaza.
Speaking in Jerusalem, Mr Brown said: "The task before us is not just a ceasefire, and it is not just an end to arms-trafficking. It is building a permanent peace - and that means security for Israel within its borders and the viability, economically and socially, of a Palestinian state.
"Permanent peace may seem a very distant prospect at the moment, but through the anguish and through the suffering and through the tears, I can see a road towards that peace."
Mr Brown said he hoped it will now be possible for Israel to withdraw its troops from Gaza and to permit the reopening of border crossings linking the enclave with the outside world, adding: "I believe that that would constitute the next stage, following the ceasefire, that would make possible the resumption of talks that are necessary for a permanent peace."
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Most people now understood the "contours" of a possible two-state solution to the Middle East conflict, said Mr Brown, adding that he believes the incoming administration of US President-elect Barack Obama - who takes office on Tuesday - will want to make the same effort to achieve a lasting peace.
