US President George Bush publicly supported Palestinian Authority Chairman Mahmoud Abbas on Thursday and praised his leadership. However in private, the differences between the US and the PA over the question of Hamas's participation in the Palestinian Legislative Council elections still remain. In a joint press conference in the White House Rose Garden, Bush demanded that the PA confront violence before the elections, but refrained from demanding that Hamas be disarmed before it is allowed to take part in the political process. He referred only to "armed gangs," and did not mention Hamas by name. PA sources said after the meeting that there are still differences of approach regarding the future of Hamas in the political system. While Abbas would like to allow it to take part in the elections even before disarming, the US is calling for steps, even if they are only symbolic ones, that will ensure the principle that politics and terror cannot mix. In their 90-minute meeting, Bush and Abbas discussed the steps taken by the PA to deal with violence in the territories and reform its security forces, but in the public appearance after the meeting, Bush adopted Abbas's motto of "One Authority, one law, one gun," without getting into the specifics of how to make sure there will only be "one gun." "The way forward must begin by confronting the threat that armed gangs pose to a genuinely democratic Palestine", Bush said, "and those armed gangs must confront the threat that armed gangs pose to lasting peace between the Israelis and the Palestinians". In previous events Bush used the term "terror groups" when he referred to Hamas and other armed organizations in the PA territories. Abbas made it clear that all the Palestinian factions could take part in the political process if they chose the route of democracy, instead of violence. "Now, all groups are under way to the electoral process, so all groups will become a part of the political Palestinian fabric. I believe this will create a new phase in the life of Palestinian people. It's a phase of democracy and pluralism in full fledge in order to be a solid base for peace in the region," he said. Bush was full of praise to Abbas in their joint press conference and repeated several times that he had chosen the way of peace and had run for office with a platform of peace. Diplomatic sources in Jerusalem downplayed the significance of the praise Bush heaped on Abbas and said nothing surprising came out of the meeting. They drew particular attention to Bush's stressing that while some have suggested he wants to see a two-state solution by the end of his term, "I can't tell you when it's going to happen. It's happening... One thing that won't happen is that the US will try to force parties to make decisions based upon the political schedule in America." The message to Abbas, according to one source, was that: "You have to role up your sleeves and start working, buddy. Otherwise you're not going to have a Palestinian state." He also dismissed the notion that Israel would be disappointed that Bush did not call on Abbas to ban Hamas from participating in elections or even refer to it by name. He said Bush was leaving the "internal matter" of who participates in elections up to the PA, but warning it that it would face the consequences of allowing armed groups to run. The source summarized: "It's your problem, and it's a problem you have to solve." In the press conference, Bush also praised disengagement from the Gaza Strip and the courage of Prime Minister Ariel Sharon. But at the same time he made it clear that "Israel should not undertake any activity that contravenes its road map obligations, or prejudices the final-status negotiations with regard to Gaza, the West Bank and Jerusalem. This means that Israel must remove unauthorized posts and stop settlement expansion. It also means that the barrier now being built to protect Israelis from terrorist attacks must be a security barrier, rather than a political barrier. Israeli leaders must take into account the impact this security barrier has on Palestinians not engaged in terrorist activities." These demands are not new and represent well known administration views. Abbas asked Bush to help the PA with rebuilding its economy and to take care of the outstanding issues of a ground link between Gaza and the West Bank, opening the Rafah border crossing and lifting roadblocks. Bush said it is important to make "quick progress" on these issues. Bush said he would ask special Quartet envoy James Wolfensohn to stay on until next spring in his role as a coordinator for rebuilding Gaza and announced that he would soon choose a replacement for the military coordinator Gen. William Ward, who is leaving the post this month. Abbas called on Israel to accept the conditions set out in the Sharm a-Sheikh agreement and to withdraw its forces to the lines they held before the violence broke out in September 2000. He said the PA is fighting violence and wants to prevent attacks. "We have worked and we will continue to work to continue to ensure the calm and maintain it. We are also intensifying our work in the field of security. We have taken active steps in imposing the rule of law and public order and banned armed demonstrations," he said. Hilary Leila Krieger contributed to this report.