French President Francois Hollande, second from left, and German Chancellor Angela Merkel, right, join other dignitaries, heads of government and heads of state as they march during a rally in Paris. (AP Photo/Francois Mori)

This post has been updated. 

The White House said Monday that it should have sent a higher-profile official to a Paris rally where 1.5 million people marched in a show of unity against terrorism.

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

The absence of President Obama and other top administration officials drew intense scrutiny on both sides of the Atlantic on Monday, with Republicans sharply criticizing the president at home and both domestic and foreign media raising questions about the dearth of U.S. presence at the event.

"We agree that we should have sent someone with a higher profile," Earnest said, "in addition to the ambassador to France."

The White House cited security concerns and the fact that the rally came together quickly, in about 36 hours. Earnest said presidential or vice presidential security for events such as the march are "onerous" and have a "significant impact" on those who attend.

Had the circumstances been different, "I think the president himself would have liked to have had the opportunity to be there," Earnest said.

A Secret Service official said the agency was not asked or notified about a potential trip to Paris.

During the White House briefing on Monday, press secretary Josh Earnest discussed the administration's decision not to send a high-level official to a march honoring the victims of last week's attack on a satirical newspaper and said the French ambassador would go to the White House later that day. (WhiteHouse.gov)

Days after terrorist attacks left 17 people dead, more than 40 leaders including French President Francois Hollande, German Chancellor Angela Merkel, Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas attended the Sunday march.

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," wrote Sen. Ted Cruz (R-Tex.) 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 event.

"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."

Michael Steel, a spokesman for House Speaker John A. Boehner (R-Ohio), said in an e-mail: "In the wake of Sept. 11, the world -- including the people of France -- rallied in support of the United States. The French should feel the same support from all freedom-loving peoples today."

Attorney General Eric H. Holder Jr. and Deputy Secretary of Homeland Security Alejandro Mayorkas were in Paris for weekend security meetings but did not attend the march. The White House announced Saturday that it will hold a counterterrorism summit next month aimed at curbing extremism in the wake of the attacks in Paris, as well as attacks by Islamists in Ottawa in October and Sydney last month.

Earnest said that the White House wants to send a "clear message, even in a symbolic context like this," that Americans stand with the French people.

"And sending a high-level, highly visible senior administration official with a high profile to that march would have done that," Earnest said.

He added that there is "no doubting" the support and allegiance the United States and France share to the "kinds of values that were under attack last week in Paris."

Earnest declined to say who decided not to send a higher-profile official, but it was "not a decision that was made by the president."

In an interview on MSNBC, the French ambassador to the United States, Gérard Araud, said there are "absolutely no hard feelings" on the part of the French government toward Washington over not sending a high-profile member of the administration to the rally.

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

“But that is why I am going there on the way home, to make it crystal clear how passionately we feel about the events that have taken place there,” he said.

The White House also pointed to a number of public showings of solidarity Obama made last week. Obama phoned Hollande, said at a speech in Tennessee that the United States stands with France and on Thursday visited the French Embassy in Washington, where he signed a book of condolences. American officials have been in touch with and aiding France on a near constant basis, the White House said.