The deprivations in Gaza have grown only more acute since Mr. Hamdallah’s boss, President Mahmoud Abbas, imposed harsh restrictions on Hamas over the summer. Mr. Abbas stopped paying for Gaza’s electricity and reduced the salaries of thousands of bureaucrats, teachers and police officers, who have been on the payroll for years though Mr. Abbas ordered them not to work for Hamas.

Water quality has become dangerously poor, the air reeks of raw sewage, and the unemployment rate is approaching 50 percent, worse among the young.

Fatah and Hamas have made many attempts at reconciliation, and even formed a government together in 2014, but within weeks that agreement fell apart and a new war between Hamas and Israel intervened.

This time, however, Hamas has responded to Mr. Abbas’s pressure by effectively daring him to step up and take responsibility for Gaza. And the new Hamas leaders — who attended a lunch on Monday with Mr. Hamdallah at the home of Ahmed Hiles, the leader of a Fatah-aligned clan that has clashed violently with Hamas — insist they are serious about making concessions in the name of unity.

“I will break the neck of anyone who doesn’t want the reconciliation, whoever he is, from Hamas or any other faction,” Yehya Sinwar, the prime minister of Gaza, told a group of Gazan youths in a speech late last week.

Mr. Hamdallah is to lead a cabinet meeting in Gaza City on Tuesday, but the real work of resolving how Gaza will be run, and when Mr. Abbas’s restrictions may be lifted, is to wait until next week, when both sides are to begin talks in earnest in Cairo.