Britain could have a new prime minister as soon as Monday.

The contest for the next leader of Britain’s Conservative Party — and, consequently, the country’s prime minister — could be over by Monday afternoon.

That’s because rules announced on Thursday by Graham Brady, chairman of a powerful committee of Conservative backbench members of Parliament, will severely restrict the number of candidates allowed to vie to succeed Prime Minister Liz Truss.

The rules will require them to have a minimum of 100 nominations by 2 p.m. Monday. Given that there are 357 Conservative lawmakers in Parliament who can nominate candidates, no more than three will be able to pass that threshold by that deadline.

If only one person has enough nominations by the deadline, that candidate will become party leader and the country’s second prime minister in two months.

If two candidates get to the 100-nomination threshold, there will be a vote to indicate which one has the most support among lawmakers. Unless the second-place candidate drops out, the two names will go before party members in an online vote that will conclude on Oct. 28.

If three meet the threshold, the balloting on Monday will eliminate one candidate, with the two top vote-getters advancing to the online vote.

In any event, this is on track to be the shortest Conservative Party leadership contest in memory.

Among the leading candidates to succeed Ms. Truss are Rishi Sunak, the former chancellor of the Exchequer who lost to Ms. Truss in the party leadership campaign over the summer; Penny Mordaunt, the leader of the lower house of Parliament; and Ben Wallace, the defense secretary.

Some also want former Prime Minister Boris Johnson back , even though his tenure was punctuated by a series of scandals. In addition, many voters see Mr. Johnson as a divisive figure. There is also uncertainty about whether his return would be welcomed by financial markets.