But the current public health crisis brings new urgency to the battle, as Democrats and some Republican state officials turn to expanded voting by mail as an important way to avoid the serious health hazard of crowded polling stations amid a pandemic.

In a pre-coronavirus world, Republicans found that the specter of voter fraud and the need for tighter voter restrictions were popular messages with segments of their base. If there was a chance that the political equation might change with the pandemic, Mr. Trump and his allies have not seemed concerned.

The president has embraced some of the most outlandishly false claims about voter fraud, at times proclaiming that the popular vote in the 2016 election — which he lost — was “rigged.” He has long impugned voting by mail, which, while more vulnerable to fraud than in-person voting, has proved overwhelmingly secure in states with mail-in elections, including Colorado and Washington State. (Mr. Trump had formed a special commission to investigate voter fraud in 2016 but it produced no evidence before he shut it down in 2018.) Even so, he applied for his own mail-in ballot in Florida in March.