For weeks, cease-fire talks have been at a standstill. Now, with the new proposal in hand, a mid-ranking delegation from Israel was planning to fly to Cairo on Tuesday to resume them — but only if Hamas agrees to attend, according to two of the officials. They spoke on the condition of anonymity to discuss the sensitive issue.

Hamas did not respond to a request for comment about whether it would send representatives to Cairo. A senior Hamas official said on social media on Monday that the group was studying a new Israeli proposal.