At least three American states have turned down Russian requests to monitor polling locations during the election on Nov. 8, as United States officials portrayed the overture as little more than a Russian public relations stunt.

Russia’s consul general in Houston, Alexander K. Zakharov, wrote letters dated in September to officials in Texas, Louisiana and Oklahoma requesting that a Russian officer be present “for a short period of time, when convenient,” with the “goal of studying the U.S. experience in organization of voting process.”

But United States officials have been wary of Russia meddling in the election, and the American government formally accused Russia of being responsible for recent hacks surrounding American political campaigns.

The Russian requests come as Donald J. Trump, the Republican nominee, has claimed that the election will be “rigged.” United States officials, including Republican leaders, have forcefully denied that claim.