Israeli officials have said repeatedly that they would not deal with Hamas, and Defense Minister Shaul Mofaz said Israel would not rule out targeted killings against Hamas leaders if they attack Israel. Israeli airstrikes in 2004 killed Hamas spiritual leader Sheikh Ahmed Yassin and his successor Abdel Aziz Rantisi.
"Whoever stands at the head of a terror organization and continues to carry out terror attacks against Israel is not immune," Mofaz told Israel's Channel 2 television.
Hamas' victory shocked Fatah, which dominated Palestinian politics for four decades. Abbas ordered an investigation into why his party lost so badly.
Marwan Barghouti, the jailed Palestinian uprising leader who was Fatah's top candidate and led efforts to reform the party, appealed for Fatah to hold a general conference to elect fresh leadership, according to a statement released by his wife, Fadwa.
He also congratulated Hamas and said Fatah would peacefully transfer power.
"We will respect the democratic process and its results and help those who won the confidence of our people," he said.
But many in the 58,000-member security force were less conciliatory and rejected any Hamas control.
"The security institution is a red line. We will not allow anyone to tamper with it," Gaza police chief Ala Hosni said. "It will remain a powerful and impartial arm that carries out the decisions of the presidency (Abbas) and that stops any infighting or civil war."
Dozens of armed police officers briefly stormed the parliament building in Gaza City, demanding the security forces remain in Fatah's hands and calling for Hamas members who killed police in fighting in recent months to be brought to justice.
In Ramallah, hundreds of Fatah activists, including gunmen and security officers, marched into Abbas' compound and prayed at the grave of Yasser Arafat.
"We came to you Abu Amar to forgive us for what happened," they chanted, referring to Arafat by his nickname.
Abbas' security force prevented the activists from approaching his office. Militants outside the walled compound shot in the air.
"We'll show them hell as an opposition, and we will turn the Palestinian Authority security forces into armed militia led by Al Aqsa," Ramzi Obeidi, a leader of the Fatah-allied Al Aqsa Martyrs' Brigades, told the crowd.
Other Fatah activists staged angry protests throughout the West Bank, including in Nablus.
"We are now no longer part of the cease-fire," an Al Aqsa gunman, Nasser Haras, told the crowd, referring to a year-old truce with Israel.
In Tulkarem, gunman Ibrahim Khreisheh warned against cooperating with Hamas. "Whoever will participate in a government with Hamas, we will shoot him in the head," he said.
Abbas has said he would ask Hamas to form the next government and Hamas officials said they wanted to meet him Sunday. Hamas, with no experience in government, reached out to Fatah to form a coalition, but Fatah officials said they preferred to be in opposition.
Outlining his group's plan for the future, Mashaal said it would work to reform the corruption-riddled Palestinian Authority and continue its resistance to Israel.
In a move likely to anger Israel, Mashaal said Hamas would release Ahmed Saadat, leader of the radical Popular Front for the Liberation of Palestine. He is being held at a Palestinian jail under Western supervision for ordering the assassination of an Israeli Cabinet minister in 2001.
President Bush told the CBS Evening News on Friday that the United States would cut aid to the Palestinian government unless Hamas, which the U.S. lists as a terror group, abolishes its militant wing and stops calling for Israel's destruction.
Speaking at the World Forum in Davos, Switzerland, former President Clinton suggested Saturday that the West should be more open to eventual talks with Hamas.
"You've got to find a way to at least open doors ... and I don't see how we can do it without more contact," he said. Hamas might "acquire a greater sense of responsibility, and as they do, we have to be willing to act on that."