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(CBS NEWS) -- Attempting to "resolve once and for all" any questions he faces regarding the 2012 attack in Benghazi, Libya, Secretary of State John Kerry has agreed to testify before the House Oversight Committee on June 12 or June 20, CBS News has learned.

Oversight Committee Chairman Darrell Issa, R-Calif., initially subpoenaed Kerry to testify before the committee on May 21, but Kerry was scheduled to be in Mexico that day. The State Department suggested that if the Oversight Committee were serious about investigating the 2012 attack, they could find better witnesses to testify (Kerry was not secretary of state at the time of the attack - Hillary Clinton was). Nevertheless, Issa last week issued a new subpoena requesting Kerry's appearance before the committee.

In a letter obtained by CBS News, State Department official Julia Frifield once again tells the Oversight committee that there are "witnesses better suited to answer questions." Still, she says that Kerry will appear "in the interest of accommodation" and asks for the committee to withdraw the subpoena commanding Kerry to appear on May 29. Kerry won't be able to appear before the committee on that date, the letter says, because he will be "fully occupied with critical diplomatic engagements" following the May 25 elections in Ukraine.

The letter says Kerry's appearance before the Oversight Committee should "remove any need" for the secretary of state to appear before the newly-formed House Select Committee on Benghazi.

Update: A spokesman for Issa said the chairman has accepted Kerry's offer to testify on June 12.

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