Hamas, considered a terrorist group by the United States, Israel and other nations, won the last parliamentary elections held in both Gaza and the West Bank, in 2006. A year later, it seized control in Gaza, forcing Fatah to retreat to the West Bank. As a result, while the international community treats Mr. Abbas as the leader of the Palestinian people, he does not represent the nearly 2 million people who live in Gaza.

A settlement between Fatah and Hamas could further muddy the prospects of a peace process with Israel that long ago stalled. When the two Palestinian factions agreed to resolve their differences two years ago, in a deal that was never fulfilled, Prime Minister Benjamin Netanyahu suspended peace negotiations rather than work with what he called a terrorist organization.

Thursday’s meeting comes at a time of tension for Mr. Abbas, whose leadership has been questioned at home and abroad. Municipal elections set by Mr. Abbas have been put off, but he has called for leadership elections within Fatah by the end of the year in an effort to head off internal rivals.

It also comes at a time of transition for Hamas. Mr. Meshal, who lives in Qatar, has announced that he will not run for another term in elections expected to be held next year. Mr. Haniyeh is considered a front-runner to succeed him.

In a public meeting in Doha, Qatar, last month, Mr. Meshal expressed regret about the takeover of Gaza in 2007. “Hamas made a mistake when it thought it was easy for it to rule the Gaza Strip alone,” he was quoted saying. “It thought that ruling Gaza would be easy, but discovered that it was hard.”