JERUSALEM, May 31 (JTA) — Mahmoud Abbas may want to make the most of the rather intensive world tour he embarked on following his White House meeting with President Bush, as he faces grave challenges once he returns to Ramallah. Both the Israelis and Abbas’ own rivals at home have their own agendas, creating a difficult dynamic for the Palestinian Authority president. Lack of progress on the Israeli track feeds frustration on the Palestinian side, and Abbas’ failure to tackle Palestinian radicals reduces Israeli motivation to continue making goodwill gestures to bolster Abbas. Since Abbas came to power Jan. 15, Israel has made a number of concessions, such as: • stopping targeted killings of Palestinian terrorist leaders; • releasing 500 Palestinian prisoners, and this week authorizing the release of another 400; • unfreezing P.A. tax money withheld during the intifada; • making plans to give the Palestinian Authority control of the West Bank city of Jenin before Israel’s withdrawal from the northern West Bank this summer; and • permitting several thousand Gaza Strip residents to work in Israel. But that’s still not enough to satisfy Palestinian demands. The prisoner issue is the most crucial, as it affects thousands of Palestinian families. Some 7,000 Palestinians are believed to be in Israeli jails, and the Palestinians want them all set free. Israel objects to freeing prisoners “with blood on their hands,” that is, who have been involved in deadly attacks. That dispute comes on top of constant bones of contention between Israel and the Palestinians — continued construction in some West Bank settlements, ongoing erection of Israel’s West Bank security fence and the continued existence of roadblocks limiting Palestinian movement. That, in turn, has intensified opposition to Abbas, six weeks ahead of Palestinian legislative elections scheduled for July 17. Here are some of the expected hurdles ahead: • Abbas has said he won’t honor his commitment to dismantle Palestinian militias, and instead will try to cajole them into disarming. But militia members are refusing to voluntarily hand in their weapons, and in some cases have clashed violently with P.A. security forces. One West Bank warlord, Zakaria Zubeidi of Jenin, announced this week that his group would not hand over its arms to the Palestinian Authority unless Israel ends its “occupation,” stops Jewish settlement and frees all Palestinian prisoners. • In an effort to disable the militias without confronting them, P.A. Interior Minister Nasser Youssef wants to enlist some 5,000 new policemen, but most of them would probably come from the militias themselves. Hamas, however, is refusing to cooperate: The Israeli daily Yediot Achronot reported last weekend that Hamas was training hundreds of Palestinians as a potential rival force to the P.A. security organs. • Political tension between Hamas and Abbas’ Fatah movement is rising ahead of elections, with growing concern that Hamas may win as much as 40 percent of the vote. Relations were further marred by disputes over the outcome of municipal elections already carried out in the Gaza Strip, with Fatah moving to annul voting in several areas where they fared poorly. • Fatah is trying hard to defer the elections until next January — long after the Israeli withdrawal from the Gaza Strip, which many Palestinians view as a victory for Hamas violence. Hamas regards Fatah’s machinations as an attempt to escape the verdict of the electorate. The Abbas-Bush summit last week gave the Palestinian leader a tail wind as he continued to Canada and North Africa. He was particularly encouraged by Bush’s statement that Israel should refrain from taking measures that might predetermine future negotiations over the Gaza Strip, West Bank or Jerusalem. But Washington pleasantries are one thing, and the harsh reality of the Palestinian territories is another. Abbas and Israeli Prime Minister Ariel Sharon are scheduled to meet in the next few weeks. The main purpose of the meeting will be to coordinate the withdrawal from Gaza, but Abbas will demand substantial Israeli gestures as well. Yediot Achronot reported last weekend that following the withdrawal, Israel will build a “safe passage” road between the Gaza Strip and West Bank, creating a sort of territorial continuum between the two parts of a projected Palestinian state. Legislator Ephraim Sneh of Israel’s Labor Party wrote this week in Ha’aretz that Israel, faced with the strengthening of Hamas, should do its utmost to strengthen Abbas. He suggested immediately releasing about 1,000 Palestinian prisoners, increasing the number of work permits to 20,000 and beginning a process of family reunification that would allow thousands of Palestinians to return to Gaza after Israel withdraws. But some politicians, including Health Minister Danny Naveh of the Likud, argued this week that even the release of 400 prisoners was too much since Palestinians are still attempting to carry out terrorist attacks and Abbas is doing little to stop them. Sharon, who wants to broaden his base of support ahead of the Gaza withdrawal, appears unlikely to further antagonize the Israeli right. He expressed disappointment with the result of last week’s Bush-Abbas summit, comments that may also reflect political constraints limiting Sharon’s maneuverability toward the Palestinians. “The Palestinians came out feeling no pressure to fight terror, and that they don’t have to take immediate action,” Sharon told members of the U.S. House of Representatives’ Appropriations Committee who were visiting Jerusalem this week. But Sneh argues that Sharon must show greater flexibility. “Israel’s choice is either a settlement with Mahmoud Abbas or a renewed war with his heirs, Hamas,” Sneh wrote.