Mahmoud Abbas spoke at Arafat's old headquarters, to which the Palestinian leader had been confined for nearly three years until just days before his Nov. 11 death at a Paris hospital. Tuesday marked the end of 40 days of mourning for Arafat.
Abbas, the PLO chief, is the front-runner in Jan. 9 elections to replace Arafat as Palestinian Authority president.
"We are standing here today to reiterate to the world that we are committed to the choice of just peace, to achieve the rights of our people," Abbas said.
Referring to Arafat, Abbas said: "We will continue the struggle to make your dream and our dream come true and to have a Palestinian child raise the Palestinian flag on the walls of Jerusalem, the capital of our independent Palestinian state."
In other developments:
Abbas said he would follow Arafat's legacy, as outlined in a speech by the late Palestinian leader in the summer. In that speech, Arafat acknowledged he had made mistakes in running the Palestinian Authority and promised government reform.
That disappointed Israeli Foreign Minister Silvan Shalom, reports CBS News Correspondent Robert Berger. In a newspaper interview, Shalom said Arafat's legacy is terrorism. Abbas has also ruffled feathers by saying he will insist on the so-called right of return of millions of Palestinian refugees to their former homes in Israel. Israeli officials say that's a recipe for the destruction of the Jewish state.
Pledging that "nobody will be above the law," Abbas said the Palestinians are moving toward democracy.
Abbas and Arafat often fought bitterly, with Arafat blocking government and security reform, and the disagreements prompted Abbas to resign as prime minister in 2003. However, Abbas has been careful not to criticize Arafat's legacy, in part because he wants to harness his enduring popularity during the election campaign.
About 250 people, including dignitaries from Jordan and Egypt, local Christian and Muslim leaders, and diplomats attended the memorial service in a hall inside the compound. Several hundred people paid their respects outside.
The end of the mourning period for Arafat fell on a day crammed with Mideast diplomacy.
British Prime Minister Tony Blair arrived in Israel late Tuesday to launch a new push for peace between Israel and the Palestinians.
Blair was to meet with Israeli and Palestinian leaders on Wednesday. He is the highest-level official to visit since Arafat's death, reflecting international optimism that with a new Palestinian leadership, peace talks can be restarted.
The Palestinians want a high-level conference that would push negotiations on the touchy issues that have stymied peace efforts in the past — Jerusalem, Jewish settlements, borders and Palestinian refugees.
The Israelis say the subject should be much more limited — reforms in the Palestinian administration, which they criticized for a lack of accountability, and failure of security forces to crack down on militant groups.
In London, the British Foreign Office appeared to back Sharon. "This meeting is about Palestine and practical reforms within Palestine," it said. No date has been set.
Sharon prefers to concentrate on his plan to remove all 21 Jewish settlements from the Gaza Strip and four from the West Bank next summer.
The Holocaust-invoking campaign by some settlers stirred an uproar in Israel, which gave refuge to large numbers of Holocaust survivors after World War II. About 250,000 survivors still live in Israel, and mention of the Nazi genocide in a public forum remains an extremely sensitive subject.
"We want to shock the nation," Miriam Freiman, a 67-year-old Holocaust survivor who lives in the Neve Dekalim settlement in Gaza.
They succeeded quickly, touching a raw nerve. Images of a Gaza woman wearing the star on her lapel ran on the front page of an Israeli newspaper, and radio shows discussed the settler campaign nonstop.
Former Israeli Chief Rabbi Israel Meir Lau denounced the initiative. "Spare us this return to the nightmares of the past and leave the Holocaust in its proper place," he said. "The deliberate murder of six million Jews is such a sacred and significant thing that it cannot be compared with absolutely anything else in the world." Lau is a Holocaust survivor.
The settlers say they're prepared to of their homes, even if it means going to prison, reports Berger. Critics say settlement leaders should be charged with incitement to rebellion.