(CBS News) — Virginia Lt. Governor Justin Fairfax is continuing to categorically deny the allegations of sexual assault against him, releasing the results of a polygraph test and offering his own telling of two separate encounters which he says he knew were “false from the first moment I heard them.” The Lt. Gov. said his attorneys have now urged the launching of an investigation in two separate jurisdictions to further probe the allegations against him and vowed to cooperate in any potential questioning that may arise.

Justin Fairfax Accuser Vanessa Tyson Describes Alleged Sexual Assault: “I Couldn’t Feel My Neck”

Fairfax announced that he voluntarily submitted a polygraph test with regards to the allegations made against him, which he claimed he “passed on the very first try.”

Fairfax faces allegations by two women including Vanessa Tyson, an associate professor of political science at Scripps College in Claremont, California, who claimed in February that Fairfax sexually assaulted her at the Democratic National Convention in Boston in 2004.

READ: Justin Fairfax Polygraph Results

In a statement on Wednesday, Fairfax alleged that Tyson got the date of their first meeting wrong at the DNC in Boston in 2004. Fairfax says he was not there on July 26th as Tyson alleges in her statement and claims he was with the former presidential candidate John Edwards at the time.

“While Dr. Tyson has stated definitively that she met, interacted, and had a conversation with me in Boston on July 26, 2004, the first day of the Convention; in fact, Senator Edwards and I were not in Boston on that date.  We did not arrive in Boston from North Carolina until the following day,” Fairfax explained.

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