Option 1: Defy calls to resign

Mr. Starmer appeared to face down his critics on Tuesday, daring them to formally challenge him if they had the support to do so. They would need to gather at least 81 Labour lawmakers to coalesce around a potential rival to trigger a leadership contest. It was unclear on Tuesday whether they had enough support to make that happen.

No contender to succeed the prime minister has so far publicly declared themselves to be a challenger, perhaps for fear of being the first to wield the political dagger and looking disloyal in the eyes of party members, who ultimately would decide on Mr. Starmer’s successor. In his remarks to the cabinet on Tuesday, Mr. Starmer warned that a leadership fight would not be good for the country and was already doing economic damage.

Option 2: Set out a timetable to resign

Dozens of Labour Party lawmakers had publicly urged Mr. Starmer to set out a timetable for his resignation to allow a contest to find his successor.

This option would postpone his departure for a few months and might provide some reassurance to financial markets about the immediate future of the government, particularly given the ongoing crisis in the Middle East.

It would effectively make Mr. Starmer a lame duck prime minister, casting him in the role of caretaker until his successor is chosen.

It would also give the party time to organize a contest to succeed him that might include Andy Burnham, the mayor of Greater Manchester, who appears to have political momentum behind him. Mr. Burnham would need to win a seat in Parliament first in a special election, something that was certain to take weeks if not months.

Option 3: Make some kind of concession

There has been speculation that Mr. Starmer could open the way for Mr. Burnham to return to Parliament, by stating clearly he would not block the mayor from running in a special election and would welcome him back into the government as a lawmaker.

Such a move could encourage supporters of Mr. Burnham — who polls suggest is currently the most popular Labour Party politician in Britain — to support Mr. Starmer for a few more months, and might therefore win the prime minister some time.

Option 4: Resign

For now, it appears that Mr. Starmer is defying calls to step down. “The Labour Party has a process for challenging a leader and that has not been triggered,” Mr. Starmer said on Tuesday, according to a statement from his office. “The country expects us to get on with governing. That is what I am doing and what we must do as a cabinet.”

There is always a possibility that he might change his mind, announce his resignation, and let the process for choosing his successor unfold as soon as possible. But even then, he would likely remain in Downing Street until that had taken place.