“We know moving forward that we will face a hostile court, that’s not new,” said Tom Perez, the chairman of the Democratic National Committee. But he indicated that it was just the beginning of a prolonged fight. “What they have done is invited further litigation, because they literally, quite literally, disenfranchised voters who had relied in good faith on the court.”

Ronna McDaniel, the Republican Party chairwoman, argued in an interview on Fox Business that the Democrats “want to take away the safeguards that ensure the integrity of the election process,” accusing them of trying to force “election reforms across the country during a time of crisis.”

The push to limit voting options is in keeping with Republicans’ decades-running campaign to impose restrictions that disproportionately affect people of color, the poor, and younger voters, under the banner of combating voter fraud — which is exceedingly rare. Democrats have more core constituencies among the nation’s disenfranchised, and both parties have long believed that easier voting measures will benefit Democrats.

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.

He has remained consistent in his opposition to mail-in voting throughout the coronavirus crisis, even as his lead health agency in the pandemic, the Centers for Disease Control and Prevention, lists postal balloting as its first recommendation to reduce crowd size at polling stations.