WASHINGTON — The Senate narrowly backed President Trump’s proposed arms sale to Saudi Arabia on Tuesday, in an unexpectedly close procedural vote that reflected mounting concern over the Saudi-led campaign in Yemen’s war.

Senators voted, 53 to 47, to pave the way to sell $500 million in precision-guided munitions to Saudi Arabia, batting back an effort to block the deal and saving Mr. Trump from what would have been a major embarrassment just weeks after he traveled to Riyadh and announced plans for $110 billion in arms sales.

Mr. Trump has painted the deal as one that will improve the kingdom’s military capability as well as create American jobs.

But an announcement on Monday from Senator Chuck Schumer of New York, the minority leader, that he opposed the sale cleared the way for a number of Democrats to join a few Republicans, including one of the resolution’s sponsors, Senator Rand Paul of Kentucky, in trying to slow down the sale.