MOSCOW — President Vladimir V. Putin has proposed a constitutional amendment banning gay marriage in what political analysts suggest is an effort to raise turnout for a constitutional referendum that could keep him in power but has so far stirred little enthusiasm among Russians.

Polls have suggested low turnout and little enthusiasm among Russians for the referendum planned next month.

Mr. Putin suggested in January a raft of changes to the country’s 1993, post-Soviet constitution that seemed to keep the door open for him to remain in power beyond 2024, when he is required to step down after his second consecutive term.

But most of the proposed changes were so deep in the legal weeds that even experts were left guessing how they would work, or why they were needed.