From left, Israel's Prime Minister Benjamin Netanyahu, Mali's President Ibrahim Boubacar Keita, France's President Francois Hollande, Germany's Chancellor Angela Merkel, EU President Donald Tusk, Palestinian President Mahmoud Abbas, Queen Rania Al Abdullah of Jordan and King Abdullah march during a rally in Paris on Jan. 11. (Philippe Wojazer/AP)

World leaders marched arm-in-arm with millions through the streets of Paris. There were long-time adversaries such as the Israeli prime minister and the head of the Palestinian Authority, and stalwart allies such as the leaders of Germany, France and the United Kingdom.

What was missing was the presence of senior official from the United States — a mistake for which the White House repeatedly apologized Monday.

“I think it’s fair to say that we should have sent someone with a higher profile,” White House press secretary Josh Earnest said Monday. The United States was represented by Jane Hartley, the ambassador to France.

The oversight, which may have been simply the result of a bungled bureaucratic process, offered insight into President Obama’s priorities and style when it comes to managing relationships with allies and adversaries on the world stage.

Obama has tended to take a cold-eyed view of war and peace that has played down the cultivation of personal relationships with fellow leaders and, at times, placed a priority on talking with enemies, said White House officials and foreign policy analysts. “He sees [foreign policy] as a giant puzzle,” a senior administration official said, “an intellectual problem to be solved.”

The approach offers a notable contrast with his predecessor, George W. Bush, who relished his relationships with European leaders, even though his foreign policy and the U.S.-led war in Iraq were frequently reviled on the continent.

Earnest declined to say who inside the White House was responsible for selecting the senior U.S. representative at the rally, though he said it was “not a decision that was made by the president.” Still, the decision offered some insight into how Obama has managed his relationships with European leaders, who have sometimes felt neglected by a White House focused on the Middle East and Asia.

“These process mistakes happen when the top leader isn’t pushing the system,” said Jeremy Shapiro, a former senior State Department official and fellow at the Brookings Institution. “The fact that the president didn’t get on the phone [to his foreign policy team] and say, ‘I’ve got to go,’ makes it more likely the process will fail.”

Several leading Republicans criticized the Obama administration for not having a more prominent presence at the rally.

“The absence is symbolic of the lack of American leadership on the world stage, and it is dangerous. The attack on Paris, just like previous assaults on Israel and other allies, is an attack on our shared values,” Sen. Ted Cruz (R-Tex.) wrote in a Time op-ed.

Sen. Marco Rubio (R-Fla.) said on “CBS This Morning” that it was a “mistake” not to send a higher-ranking U.S. official to the Paris rally.

“I understand that when the president travels, he brings with him a security and communications package which is intense. And I understand you drop that into the middle of something like this, it could be disruptive,” Rubio said. “There’s a plethora of people they could have sent. I think in hindsight I hope that they would have done it differently.”

The White House said that the short planning window for the march, which came together in just 36 hours, would have made it almost impossible for Obama to attend without disrupting the event. Had the circumstances been different, “I think the president himself would have liked to have had the opportunity to be there,” Earnest said.

Even though the president did not attend the rally, White House officials noted that Obama phoned French President François Hollande, spoke publicly about the attacks and made a condolence stop Friday at the French Embassy. Top administration officials stayed in touch with their French counterparts on a “minute-by-minute” basis throughout the attacks, White House officials said.

Secretary of State John F. Kerry has announced that he will visit Paris on Thursday; he was in India during Sunday’s rally. Kerry brushed aside the criticism, calling it “quibbling a little bit,” and said many embassy staff, including Hartley, attended the march.

Kerry said his stop in Paris will “make it crystal clear how passionately we feel about the events that have taken place there.”

For all the hubbub in Washington, the supposed snub caused few ripples in Paris, where attention remained focused Monday on the historic nature of Sunday’s march — and the continued security threat facing the nation.

During the rally, most French hardly seemed to notice the absence of a prominent U.S. representative. And many had felt ambivalent about the presence of global leaders in the first place, given the dubious human rights records of some who attended and the desire of participants to make the march about the unity of the French people, rather than about politics.

“I consider these heads of state to be taking part in my march,” said Thierry, a 56-year-old painter, who declined to give his last name because of fears of terrorism. “I’m not taking part in theirs.”