LONDON — Talks on a compromise Brexit plan between Prime Minister Theresa May of Britain and the opposition Labour leader, Jeremy Corbyn, hit a snag on Friday, just as Mrs. May sought a nearly two-month delay in the deadline for leaving the European Union.

Labour leaders said Mrs. May had so far refused to budge from her original plan, but the government said it was still prepared to propose changes.

The developments illustrated the challenges confronting the leaders in reaching an agreement for Britain’s withdrawal, with both Mrs. May and Mr. Corbyn facing difficulties within their parties if they compromise.

News of the deadlock came on the same day Mrs. May asked for a second extension of the deadline for departure, to June 30. The original March 29 deadline had been extended once, to April 12 — one week away.