JERUSALEM — With Egypt brokering a reconciliation between the two rival Palestinian factions, President Trump’s special envoy to the Middle East visited Cairo on Thursday to help move those talks along while trying to ensure that the Egyptians do not take them in a direction unacceptable to the United States and Israel.

Hamas, the militant Islamic group that seized power in the Gaza Strip in 2007 and has run it ever since, agreed in Cairo last week to return administrative control of the impoverished coastal territory to the Palestinian Authority, led by President Mahmoud Abbas.

The Oct. 12 agreement calls for the Palestinian Authority to lift sanctions that it imposed on Gaza this year to pressure Hamas by cutting electricity supplies to a few hours a day and slashing payment of government salaries. Hamas, in turn, is to give the authority control of the Rafah border crossing with Egypt, opening up a critical lifeline for imports and for outside travel.

But the pact was really an agreement to start talking: The more troublesome issues between Hamas and Mr. Abbas’s Fatah faction — including the merger of two separate work forces in Gaza, and what is to become of the estimated 25,000 Hamas fighters, their arsenal of rockets and network of tunnels — were left for later.