He also said, “We’re talking about a march that came together with essentially 36 hours’ notice.”

Still, on the day after a rally that drew more than one million people and some 40 heads of state following terrorist attacks in Paris, the lack of a top American official became another example of what critics call tone-deafness by the president and his senior staff.

Even some Democrats said they were mystified by the lapse.

“I was puzzled that the United States did not have a high-level representative participating in the march,” said former Representative Lee H. Hamilton of Indiana, a Democrat who sits on the president’s Homeland Advisory Council and directs the Center on Congress at Indiana University. “It’s a missed opportunity. This was a world-shaking event for Paris, and France has been a good ally of ours for decades. We should have been more visible in our support for an ally under duress.”

Reince Priebus, the chairman of the Republican National Committee, took to Twitter to criticize the president. “Obama declining to show solidarity with over three million in France is beyond crass, even for this administration,” he wrote in a post.

The march followed the shootings of 17 people in separate attacks last week at the satirical newspaper Charlie Hebdo and at a kosher supermarket. Leaders at the rally included Prime Minister David Cameron of Britain, Chancellor Angela Merkel of Germany, Prime Minister Benjamin Netanyahu of Israel and President Mahmoud Abbas of the Palestinian Authority. Official administration schedules said that Mr. Obama was at home at the White House on Sunday, and that Mr. Biden was at his residence in Wilmington, Del. Neither had public events, and aides declined Monday to say how the president spent his day.

Senator Ted Cruz, Republican of Texas and a potential presidential candidate, called Mr. Obama’s absence “symbolic of the lack of American leadership on the world stage, and it is dangerous.”