Millions of Americans will cast their ballots on Tuesday under intense scrutiny both from vigilantes who fear the election will be rigged and from thousands of voting rights advocates who fear the tally will be distorted by intimidation and, perhaps, the suppression of a minority vote that may be crucial to the outcome.

On one side are groups like the Oath Keepers, one of dozens of right-wing and militia groups responding to Donald J. Trump’s warnings about a stolen election. The organization has issued a nationwide “call to action” to its members, urging them to go “incognito” to polling stations on Election Day to “hunt down” instances of fraud.

On the other side are more than 100 civic and legal groups, claiming at least 10,000 volunteers, and perhaps many more. They plan to deploy at polling places nationwide to watch for signs of voter intimidation and other roadblocks to voting. Election officials and observers say they are hoping for an orderly final day of voting, but they are girding for the possibility of fights, intimidation and, perhaps, worse.

Adding to the anxiety is fear of Election Day hacking, perhaps by foreign interests.

“I would say this is the most frightening election period I can remember in my adult life,” said Richard L. Hasen, an election law expert and professor at the University of California, Irvine.