LONDON — British leaders agreed on Monday to allow Parliament to debate, amend and vote on the terms of its exit from the European Union, in a concession to rebellious lawmakers who have demanded more power over the process.

The Brexit minister, David Davis, made the announcement just as Parliament was preparing for debates Tuesday over a bill on Britain’s withdrawal from the European Union, or Brexit. In eight scheduled debates, lawmakers will consider 186 pages of amendments, including some that would stop the government from concluding a deal without their express approval.

Mr. Davis’s announcement seemed intended to soften lawmakers’ resistance ahead of the debates and speed the passage of the withdrawal bill, which would transfer existing European law to the British statute books.

“Parliament will be given time to debate, scrutinize and vote on the final agreement we strike with the European Union,” he said. “This agreement will only hold if Parliament approves it.”