WASHINGTON — In a rare admission of error, the White House said Monday that President Obama or another high-level representative should have joined dozens of world leaders at an anti-terror rally in Paris.

While leaders from Europe, the Middle East and Africa linked arms for Sunday’s march through the boulevards of Paris, the United States was represented by its ambassador to France. Attorney General Eric Holder was in Paris for security meetings but did not attend the march.

“It’s fair to say we should have sent someone with a higher profile,” said White House spokesman Josh Earnest. The administration also announced that Secretary of State John Kerry, who was on a long-planned trip to India on Sunday, will visit France later this week.

The White House appeared to have been caught off guard by both the scope of international representation at the rally and the criticism of the decision to send only Ambassador Jane Hartley. Monday’s admission of error seemed aimed at blunting criticism that the decision was tone-deaf or disrespectful of the longstanding U.S. alliance with France.

France has been on edge since the attacks that left 17 people dead and heightened fears about the spread of terrorism in the West. Three of the gunmen, who claimed allegiance to Islamic extremist groups, were killed by police, though French authorities said Monday that as many as six terror cell members might still be at large.

Before the White House acknowledged its misstep, Florida Republican Sen. Marco Rubio said the administration had made a mistake by not at least sending Holder or Kerry to attend Sunday’s rally. And Sen. Ted Cruz, R-Texas, said it was an example of Obama’s team keeping allies at a distance.

“Where was the president? Where was the vice president? Where was the secretary of state? Where was the attorney general, who had been there moments before, but chose to get on a plane and fly back home?” Cruz asked Monday during a speech at the conservative Heritage Foundation.

Some Obama administration officials, too, privately expressed frustration that a high-level U.S. representative did not participate in the march. Earnest said the White House took the blame but said Obama himself was not personally involved in the decision. Earnest would not say who was responsible for deciding the administration’s participation in the event.

The fallout from the weekend rally underscored the degree to which the Obama White House has sometimes struggled with the potential importance of symbolic gestures.

“Part of this job is the theater of it,” Obama said last summer amid criticism that he had gone golfing just minutes after speaking about the beheading of an American journalist in Syria. “It’s not something that comes naturally to me. But it matters. And I’m mindful of that.”

Earnest suggested it was the elaborate security apparatus required for presidential travel that prohibited Obama, as well as Vice President Joe Biden, from going to Paris on relatively short notice.

“There’s no doubt that had the president or vice president, on this very short time frame, gone to participate in this event that took place outdoors with more than a million people in attendance, that it would have significantly impacted the ability of those who attended the march to participate in the way they did yesterday,” he said.

Planning for presidential travel overseas often begins months in advance, and security personnel typically arrive days ahead of Obama. However, trips are occasionally pulled together more quickly, including last year when Obama went to South Africa for a memorial service following the death of Nelson Mandela. Vice presidents can also typically travel with a lighter security footprint.

Dozens of world leaders did attend the march in Paris on Sunday, including Israeli Prime Minister Benjamin Netanyahu, Palestinian President Mahmoud Abbas, British Prime Minister David Cameron and German Chancellor Angela Merkel. More than 1 million people joined in the march, which French officials called the largest demonstration in their country’s history.

Smaller marches were held in cities around the world, including one in Washington, just a few blocks from the White House. Assistant Secretary of State Victoria Nuland attended that event.

Earnest said that despite the lack of a high-level U.S. official at the Paris march, there should be no doubt about Obama’s commitment to America’s alliance with France. He noted that Obama had spoken to French President Francois Hollande following the initial attack and had visited the French Embassy in Washington to sign a condolence book.

The French ambassador to the U.S. met with Obama’s top counterterrorism adviser at the White House on Monday. The White House said Ambassador Gerard Araud thanked the U.S. “for unwavering U.S. support to France in the aftermath of the attacks,” particularly in intelligence-sharing and law enforcement cooperation.