Kerry was subpoenaed to testify on May 29, but the letter said prior commitments would prevent his appearance. Kerry offered two other dates - June 12 or June 20 - for his testimony, and asked the committee to withdraw its subpoena, the letter said.
If Kerry testifies before the House of Representatives Oversight Committee, the letter said, it should remove any need for the secretary to appear before a House Select Committee that was formed recently to look into the Benghazi incident.
Four Americans, including U.S. Ambassador Christopher Stevens, were killed in the attacks.
House Republicans have launched multiple investigations into the Obama administration's handling of embassy security in the run-up to the attack and the steps it took in the aftermath.
Democrats have accused Republicans of creating the panel for political purposes, including keeping the spotlight on Hillary Clinton, Obama's secretary of state at the time of the Benghazi attack. Clinton, a Democrat, is weighing a 2016 run for president.
Republican House Speaker John Boehner has insisted that the special committee will conduct a "serious, fact-based inquiry."