President Bush and Israeli Prime Minister Ariel Sharon came out of their Tuesday afternoon meeting pleased with their discussions and agreeing to return former CIA Director George Tenet to the region to negotiate a security framework needed to begin the peace process between Israelis and Palestinians.

The two men could not agree on whether the process should include moving toward Palestinian statehood, but they glossed over their differences at a White House press conference.

"One of the things that I think is important, the prime minister has discussed this as well, is for us to immediately begin to help rebuild a security force in Palestine that will fight terror, that will bring some stability to the region," Bush told reporters after the meeting.

The conference came as a suicide attacker exploded a bomb in a pool hall and nightclub in the Israeli town of Rishon Letzion. Police said more than 15 people were killed and another 60 injured. Hamas claimed responsibility for the bombing.

Bush and Sharon did not address the bombing though National Security Adviser Condoleezza Rice said the two were aware of the attack and Bush expressed his "disgust" that another life was lost.

The attack was not coincidentally timed to the meeting. In response, Sharon decided to leave the United States early, where he has been at his fifth meeting with the president. He had been scheduled to meet later with congressional leaders, but those talks were canceled, an Israeli spokesman said.

Bush and Sharon have very different agendas. Sharon was in Washington to push a tough sell: no negotiations with Palestinian leader Yasser Arafat, no negotiations on Palestinian statehood until the Palestinians prove they are not a security threat, and no negotiations until the Palestinians establish democratic institutions.

Bush has said repeatedly that Arafat is the chosen representative of the Palestinian people and there's no choice but to deal with him, though he recognized that Arafat needs to do a better job in leading his people.

"I want to reiterate what I have said and will continue to say: There are responsibilities. If people truly want for there to be peace, people have to assume their responsibilities for peace," he said.

Bush did say that he is looking for a unified Palestinian security apparatus. That would mean instead of several Palestinian police and military operations, there would be a single command that would fight terror and bring stability to the region. He added that security also extends to the democratic institutions that govern the Palestinians.

"The Palestinians need to develop a constitution, rule of law, transparency. They've got to have a treasury that is able to battle corruption," he said.

The administration also wants to see Israel moving toward a land-for-peace deal with Arafat's Palestinian Authority.

Asked if statehood is an option, Sharon said it was premature to discuss such an arrangement.

"I think that what we have to concentrate on now is making every effort that real reform will take place," Sharon said.

The administration has not decided on a formula for peacemaking and was soliciting views of Arab and Israeli leaders trying to determine what can be achieved.

Secretary of State Colin Powell said Monday that one approach under consideration was a series of "way stations," or interim talks, such as an international conference this summer.

While Israel wants to take an incremental approach, it is also widely publicizing documents seized during the military offensive which they say show Arafat was intimately involved in directing terrorist acts against Israelis and the Saudis gave money to the families of suicide bombers. The revelation was aimed at further de-legitimizing Arafat.

Saudi's foreign ministry spokesman accused the Israelis of trying to derail peace talks and said the international conferences mentioned by Powell must put a new peace plan on the table.

"What we are waiting for is a statement from the Israeli prime minister that he will freeze settlements and that he will completely withdraw from the Palestinian territories," Adel Al Jubeir said.

Sharon said that Israel is now able to withdraw from the Palestinian territories because the anti-terror operation it conducted in the West Bank achieved much of what it set out to do and gave the parties a chance to start and move forward.

The comments were made, however, before the pool hall explosion. Bethlehem also remains in standoff mode between Israeli defense forces and Palestinian holdouts in the Church of the Nativity. A deal had been reached to exile 13 alleged Palestinian outlaws, but Italy refused to accept them into the country.

Bush and Sharon did agree on the need to rebuild the structure of the Palestinian authority. The White House says that the only Palestinian state that can succeed alongside Israel must have democratic leadership, an end to corruption, and a market based economy.

White House Press Secretary Ari Fleischer said Tuesday that unless those conditions come to pass, Israel will remain bordered by an unstable country, and that is a prescription for continued problems.

Fox News' Jim Angle, Wendell Goler and The Associated Press contributed to this report.