WASHINGTON – Israeli and Palestinian leaders formally reopened peace talks Thursday by setting a work plan for the next year, but adjourned without progress on the key issue of Israeli housing construction, which threatens to quickly undermine the negotiations.

Meeting at the State Department, Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Mahmoud Abbas agreed to meet again on Sept. 15 and to work out an outline of a peace deal as the first step to a final accord by next September.

The two leaders, who met face to face for the first time after a 20-month interruption, plan to meet every two weeks.

Secretary of State Hillary Rodham Clinton, who hosted the four hours of talks, praised the two leaders.

“The decision to sit at this table was not easy,” she said. “We’ve been here before and we know how difficult the road ahead will be.”

But diplomats said officials on both sides as well as their American colleagues remain deeply anxious over the construction dispute. A partial Israeli moratorium ends on Sept. 26 and Jewish leaders are reluctant to extend it. But Palestinians have threatened to walk out on the talks if construction resumes.

U.S. officials have urged Israeli and Palestinian leaders to stop publicly declaring their positions, in hopes that it will be easier for each to give ground in a few weeks, according to diplomats who declined to be identified because of the sensitivity of the talks.

U.S. officials are hoping that as the talks gain momentum in the coming weeks, it will give officials on both sides the political cover to make compromises that, at the moment, are likely to inflame their constituencies.

As the peace talks continue, it also will become harder for the leaders to break off their participation, diplomats noted.

Yet diplomats and outside observers say it remains difficult to see how a compromise could be reached.

Under one proposal, by Israeli Deputy Prime Minister Daniel Meridor, Israel would allow construction only in the large settlement blocs in the West Bank that are expected to be annexed to Israel in a final peace deal.

But critics say it would be tough to sort out precisely which blocs would be headed for annexation.

Another possibility is for Israel to privately agree to limits while publicly announcing that the moratorium is over. Netanyahu reportedly agreed to such a deal in recent months regarding construction in the disputed city of Jerusalem.

Despite U.S. pressure, Palestinian officials insist their position on the issue is firm. Some officials privately suggested they are willing to face the political consequences of publicly embarrassing President Barack Obama by breaking off the talks.