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

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,” White House spokesman Josh Earnest said. 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 by 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.

Watch video: US criticized for absence of leaders at Paris march

Mr. Earnest said that despite the lack of a high-level U.S. official at the Paris march, there should be no doubt about Mr. Obama’s commitment to America’s alliance with France. He noted that Mr. 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. also planned to visit the White House Monday to meet with the Mr. Obama’s top counterterrorism adviser.

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 the Sunday rally. And Sen. Ted Cruz, a Republican, said it was an example of Mr. Obama’s team keeping allies at a distance. Both men are possible presidential contenders in 2016

“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?” Mr. Cruz asked on 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. Mr. Earnest said the White House took the blame but that Mr. Obama himself was not personally involved in the decision. Mr. Earnest would not say who was responsible for deciding the administration’s participation in the event.

Mr. Earnest suggested it was the elaborate security apparatus required for presidential travel that prohibited Mr. Obama, as well as Vice President Joe Biden, from travelling 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 Mr. Obama. However, trips are occasionally pulled together more quickly, including last year when Mr. Obama travelled to South Africa for a memorial service following the death of Nelson Mandela. Vice Presidents can also typically travel with a lighter security footprint.

The French Ambassador to the U.S. met with Mr. 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.

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