Secretary of State Hillary Rodham Clinton on Monday embarked on her first overseas trip since last month's deadly attack on the U.S. Consulate in Libya, traveling to Peru for a conference on women's empowerment amid the lingering political drama in Washington over the Obama administration's handling of the incident.

Clinton arrived for the long-planned women's event in Lima after another weekend of criticism from Republicans over the Obama administration's initial explanation of the Sept. 11 attack and security at the consulate in Benghazi, where the U.S. ambassador and three other Americans died.

Her arrival coincided with a call from the chair of the House Foreign Affairs Committee, Rep. Ileana Ros-Lehtinen, R-Fla., for Clinton to answer more questions about what was known about the security situation in Libya in the period leading up to the attack as well as the State Department's priorities on paying for and protecting diplomatic missions abroad.

Ros-Lehtinen took issue with State Department officials who called the assault on the Benghazi consulate by many dozens of heavily armed militants "unprecedented." She argued that the threat of such an attack, particularly on the anniversary of Sept. 11, 2001, "cannot be news to anyone" after strikes on other U.S. diplomatic missions over the past two decades.

"How can anyone consider such an attack to be unprecedented?" Ros-Lehtinen asked Clinton in a letter released by the congresswoman's office in Washington.

Her questions came after numerous Republicans took to the Sunday talk shows to criticize the administration for its changing explanations of the attack and response to it.

Sen. Lindsey Graham of South Carolina, a long-time point man for the GOP on national security issues, accused President Barack Obama's aides of deliberately covering up the details of the attack so that voters couldn't question Obama's handling of the war on terror.

Graham said he believes the administration knew within 24 hours of the assault that it was a coordinated militia attack and was not tied to other anti-U.S. protests across the Middle East. According to Graham, the administration suggested otherwise so voters wouldn't think al-Qaida remained a threat.

"They're trying to sell a narrative, quite frankly, that (the) wars are receding and that al-Qaida has been dismantled," said Graham, a member of the Senate Armed Services emerging threats and capabilities subcommittee, in an interview on CBS "Face the Nation."

"And to admit that our embassy was attacked by al-Qaida operatives ... I think undercuts that narrative," he added.

Clinton has vowed a full and open investigation on the incident. The administration initially described the attack as a more violent version of the protests that broke out across North Africa and the Middle East over a California-produced film that ridiculed the Prophet Muhammad. Administration officials amended those statements days later to call it a terror attack, likely by al-Qaida-linked militants, because they said intelligence became clearer in the aftermath.

In Peru, Clinton is meeting with President Ollanta Humala and attending a conference on "Women as the Drivers of Social Growth and Inclusion."

She returns to Washington on Tuesday.