The move potentially gives Mr. Cuomo, who is seeking a third term, a valuable perch from which to receive votes in the general election against the Republican candidate, Marcus Molinaro, and could help the W.F.P. assure its own survival as a viable third party in the state.

Under state law, any party that fails to get 50,000 votes in an election for governor loses its place on the ballot until the next election for governor, effectively ending its influence in elections for four years.

It was not immediately clear whether Mr. Cuomo — who has had a fraught relationship with the Working Families Party — would accept the ballot line, and the W.F.P. set a deadline of 5 p.m. Friday for the governor to accept the offer. Mr. Cuomo’s campaign declined to comment.

Major-party candidates in New York commonly appear on as many ballot lines as possible in order to maximize their tally on Election Day. Under state law, candidates in New York are able to collect votes on multiple party lines, which are counted cumulatively. Mr. Cuomo, 60, a lifelong Democrat, is expected to appear on at least one other minor party line — that of the Independence Party — in November.

Despite the move to endorse Mr. Cuomo, there was still open criticism of him and his sometimes heavy-handed tactics, with battle lines sharply drawn over political purity (as represented by Ms. Nixon) versus pragmatism (as represented by Mr. Cuomo).