Appearing on a nationally broadcast interview today, Denis McDonough noted that the White House has said that it regrets the misstep. The decision, he said, "rests on me. That's my job."
The Obama administration came under sharp criticism for not sending a high-level representative to the march, which was attended by more than 40 world leaders and more than a million people.
The US ambassador to France, Jane Hartley, was the top American official at the rally.
The Paris rally was attended by several world leaders, including Israeli Prime Minister Benjamin Netanyahu, Palestinian President Mahmoud Abbas, British Prime Minister David Cameron and German Chancellor Angela Merkel.
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It followed terrorist attacks on a French newspaper and a kosher supermarket that killed 17 people.
Republicans quickly criticized the decision to send only Hartley to the rally. Sen. Marco Rubio said the administration had made a mistake by not at least sending Attorney General Eric Holder or Secretary of State John Kerry to attend the march. Holder was in the city at the time, although Kerry was holding talks in India.