Straw planned two days of talks to press Israelis and the Palestinian Authority to take steps to ensure the smooth running of a 9 January presidential election to choose Arafat's successor.
But no breakthroughs are expected in a visit seen by both sides as a bid by UK Prime Minister Tony Blair, plagued at home by political fallout from the Iraq war, to show he is giving priority to the pursuit of Middle East peace.
Britain and the rest of Europe are considered junior partners to the United States, which is showing tentative signs of reviving its long-dormant role as one of the peacemakers between Israel and the Palestinians.
Straw's mission could build on this week's visit by US Secretary of State Colin Powell, who secured an Israeli pledge to ease its military grip on the occupied West Bank to make it easier for Palestinians to campaign and cast ballots.
Though Washington shunned Arafat as an "obstacle to peace", Britain kept ties with him while demanding sweeping reforms that were never carried out.
PLO chief Mahmud Abbas (R) is
seen as a US and Israeli favourite
Arafat, the long-time symbol of Palestinian nationalism, died in a Paris hospital on 11 November.
"I have come to listen to see what the Israeli political groups are doing to take advantage of the new circumstances," Straw said after talks with veteran peacemaker Shimon Peres, head of the main opposition Labour Party.
He later met Foreign Minister Silvan Shalom and is to end his day with Prime Minister Ariel Sharon, who has promised to loosen restrictions on Palestinians in the West Bank, but has stopped short of committing to a troop pullback for the vote.
Sharon has not succumbed to international pressure for confidence-building gestures to the Palestinians' interim leadership, saying they must first confront other Palestinian groups who are part of a popular uprising against Israeli occupation.
"I shall be talking to Palestinians about the efforts they will be making to improve security and to establish the elections," Straw said.
British officials said Straw wanted to hear how Israel would help ensure the elections' smooth running.
Israeli army checkpoints
Palestinians say a free vote will be impossible while Israel keeps army checkpoints around their cities.
Palestinians say Israeli army
checkpoints are hampering peace
Israel says these checkpoints and other measures are important for "security" reasons.
Officials said Straw would also press the Palestinians, on a visit to the West Bank city of Ram Allah on Thursday, to reform their security services.
He will meet Palestinian Prime Minister Ahmad Quraya and Palestine Liberation Organisation head Mahmud Abbas, a US and Israeli favourite to win January's presidential election.
Straw will lay a wreath at Arafat's grave.
The coincidence of Arafat's death and the end of the US election race has sparked talk of a new opportunity to try to bring Israelis and Palestinians back to the negotiating table.
President George Bush has pledged to use US clout to help create a Palestinian state in his second four-year term.
Straw declined comment on Wednesday on media reports that Blair planned to visit the region in December.
Last word for Sharon
The Israeli prime minister cancelled a meeting on Wednesday with visiting British Foreign Secretary Jack Straw, citing health reasons, an official in the prime minister's office said.
The meeting has now been pushed back a day, scheduled for Thursday.
Sharon had been due to meet Straw at 1500 GMT to discuss steps to help Palestinians elect a successor to late president Yasir Arafat in January.
International mediators hope the 9 January election will help revive Israeli-Palestinian peace talks.
Sharon is under pressure to ease
"The prime minister is perfectly well, but he has lost his voice and the meeting (with Straw) has been cancelled," the official said.
He said it was not known if Sharon would try to reschedule the meeting on Thursday, when Straw was to wrap up his two-day visit with a round of talks with Palestinian leaders.
Straw hoped to build on a Monday visit by outgoing US Secretary of State Colin Powell, who obtained an Israeli pledge to ease a military clampdown in the occupied West Bank to make it easier for Palestinians to campaign and cast ballots.