State Department spokeswoman Victoria Nuland said the department had accepted the resignations of four people: Boswell and three others she declined to identify.
The resignations did little to mollify lawmakers who will question Burns and Nides and who insist that Secretary of State Hillary Rodham Clinton testify in the coming weeks despite her plan to leave the administration.
Clinton had been scheduled to testify before the committees, but canceled after fainting and sustaining a concussion last week while recovering from a stomach virus. Clinton is under doctors' orders to rest.
"She is ultimately responsible for the department and U.S. posts around the world. Her testimony before the Senate Foreign Relations Committee is indispensable to any effort to address this failure and put in place a process to ensure this never happens again," Sen. Marco Rubio, R-Fla., said.
The report's findings underscore a fundamental problem the State Department has been trying to address for decades without success: how to protect diplomats while allowing them to perform their duties to reach out to foreign governments and the public to promote U.S. interests and values.
In a letter to Congress, Clinton said "our diplomats cannot work in bunkers and do their jobs."
"When America is absent, especially from dangerous places, there are consequences," she said. "Extremism takes root, our interests suffer, and our security at home is threatened. We must accept a level of risk to protect this country we love and to advance our interests and values around the world."
The American Foreign Service Association, the union that represents U.S. diplomats, said it agreed. It welcomed the findings and accepted the board's 29 recommendations for improving embassy security, particularly at high-threat posts.
"There is inherent risk in the practice of active and effective diplomacy, and our diplomatic personnel will always be exposed to a degree of harm in the line of duty," the association said in a statement. "It is our responsibility to do all we can to minimize the risk and balance it with the importance of the mission and to ensure that the missions we undertake have the personnel and financial resources to achieve policy goals."
At the State Department, retired Adm. Mike Mullen, co-chairman of the review board, said the mission's security fell through bureaucratic cracks caused in part because buildings were categorized as temporary. Budget constraints also led some officials to be more concerned with saving scarce money than in security, the report said.
The other co-chairman, retired ambassador Thomas Pickering, said personnel on the ground in Benghazi had reacted to the attack with bravery and professionalism. But he said the security precautions were "grossly inadequate" and the contingent was overwhelmed by the heavily armed militants.
"They did the best they possibly could with what they had but what they had wasn't enough," Pickering said.
Pickering and Mullen spoke shortly after briefing members of Congress in private.
Associated Press writer Matthew Lee contributed to this report.