FBI agents are making their way to Tunisia to interview a suspect detained there in the Libya consulate attack, sources tell Fox News, after Tunisian officials initially refused to grant the U.S. investigators access to the man.

Tunisian authorities agreed to let the FBI question Ali Ani al Harzi only if it is done "under Tunisian sovereignty," a condition apparently being cited in recognition of domestic pressure in the North African country.

The latest development comes after an intervention by Sen. Lindsey Graham, R-S.C., who wrote to the Tunisian authorities about the lack of access. It isn't clear what pressure the Obama administration had been applying.

U.S. Ambassador Chris Stevens and three other Americans were killed in the Sept. 11 attack on the consulate in Benghazi, Libya. The local Libyan extremist group Ansar al-Sharia has been blamed for the strike, which has become a top Republican criticism of the Obama administration in final weeks of the presidential race.

Harzi was arrested at an airport in Turkey in the days after the attack and transferred to Tunisian custody, but until now, U.S. interrogators have not had access to him. Even so, U.S. intelligence agencies have confirmed through facial recognition technology that the Tunisian was present the night of the consulate attack.

“We are very pleased the Tunisian government is working with American investigators to allow in person access to Ali Ani al Harzi," Graham said Friday. "Under this arrangement the interviews will be under Tunisian supervision and consistent with their sovereignty and meets the needs of our investigative team."

Graham expressed optimism that this "welcome breakthrough" will help the investigation advance.

“It is unfortunate it has taken this long to get an in-person interview, as time is of the essence in cases like this," he said. "We hope our interview of Ali Ani al Harzi will bear fruit and we can bring to justice those responsible for killing Ambassador Stevens and three other Americans."

Fox News' Catherine Herridge and Jennifer Griffin contributed to this report.