Mahmoud Abbas, the newly elected president of the Palestinian Authority, has to tackle several major issues in order to raise hopes for the Israeli-Palestinian peace process.

Experts on Middle Eastern affairs say Mahmoud Abbas faces enormous internal and external challenges in the weeks and months ahead. These include fighting corruption, improving the economic well being of the Palestinians, reforming the security apparatus, not to mention relations with Israel.

But analysts say Mr. Abbas faces an even greater test: how to deal with extremist groups such as the Al-Aqsa Martyrs Brigade, the Islamic Jihad and the largest group, Hamas, the Islamic Resistance Movement. All three are on the U.S. State Department's list of terrorist organizations.

Walter Reich, Middle East expert at George Washington University, says Hamas' aim is clear.

"Hamas has absolutely no hesitation to say our [their] goal is the end of Israel. There should be no Israel and that Palestine, when we talk about Palestine, we're talking about the whole area from the river, namely the Jordan River, to the sea, the Mediterranean," he said. "There is no place for Israel. And we're going to get rid of it one way or the other, no matter how long it takes. And we're going to continue fighting. We're going to continue doing whatever we can and in whatever way we can to blow up Israelis wherever they may be: whether they're in the West bank, whether they're in Gaza, whether they're in Tel Aviv, or Jerusalem, or Haifa or wherever."

Many analysts say that goal is diametrically opposed to Mr. Abbas' vision. One of those experts is Fawaz Gerges, professor of Middle Eastern studies at Sarah Lawrence College in Bronxville, New York. He says the new Palestinian leader believes the years of militant attacks on Israel have hurt his people's cause.

"Mahmoud Abbas believes that the militarization of the intifada [Palestinian uprising] four years ago has done a great deal of damage, not only to the Palestinian cause and society, but even to the moral compass of the Palestinians. He believes that the armed struggle does not take the Palestinians too far and as such, there is an urgent need for a new paradigm [example], a paradigm based on negotiations, based on bargaining, on coalition building, on appealing to at least the unity and empathy of the international public opinion, including European and American public opinion," he added.

The Israeli government has called on Mr. Abbas to crack down on terrorist groups. In the past few days, Islamic militants claimed responsibility for rocket attacks and a suicide bombing against Israeli targets. Israeli leaders have said their patience is running out: a reference to possible major military action in the Gaza strip. Following the recent attacks, a senior Palestinian commander said security forces will be deployed in Gaza to try to prevent attacks by militant groups.

Nathan Brown, a Middle East expert with the Carnegie Endowment for International Peace, a Washington D.C. research organization, says there are two ways Mr. Abbas could stop attacks by extremist elements.

"One is through brute force and the other is by trying to talk these groups out of it. Mahmoud Abbas has made clear that he doesn't want to use brute force; he doesn't think he has the ability and he doesn't think it would stick. He doesn't have the political will to do it and for whatever reason he is not going to follow that path. Instead, he is going to try to talk them into a ceasefire," said Mr. Brown.

Hamas and other militant groups have said they would consider a ceasefire only if Israel agrees to stop its raids on Palestinian areas and ends its targeted killings of wanted Palestinians. Israel has rejected those demands.

Mr. Gerges from Sarah Lawrence College says Hamas and other militant groups have the means to undermine, if not sabotage, Mr. Abbas' view that violence is counterproductive.

"The question is how will Mahmoud Abbas deal with Hamas and [Islamic] Jihad. This is a serious issue. This is not very simple at all because Mahmoud Abbas is at the same time opposed to using Palestinian security forces to crack down against Hamas. He has made it clear that he is against any kind of civil war within Palestinian society," he said. "So this is why, if you don't believe in a military crackdown, against the militant elements of Hamas and Jihad, your options are very limited. And the question is: what if Hamas or Jihad escalate, or let's say launch a major suicide bombings against Israel? What would Mahmoud Abbas do?"

That view is echoed by Seth Jones, Middle East expert with the Rand Corporation, a Washington DC research organization.

"One of the real dilemmas for Abbas is going to be when the first terrorist attack occurs in Tel Aviv or Jerusalem or somewhere in Israel: a bus bombing, for example. What is going to be the response of Abbas, because the Israelis, of course, are going to want him to crack down on groups like Islamic Jihad and Hamas," asked Mr. Jones. "And he is going to be in a tough position, especially if there hasn't been much progress on the Israeli-Palestinian peace front."

Many experts say progress on the peace front is essential for Mr. Abbas to succeed in getting militant groups to lay down their arms. If there is no positive movement in the near future, analysts say this may simply embolden militant groups to continue their attacks and thus make the search for peace even more elusive.