The American regulatory agency filed the complaint on Monday in federal court in Washington, DC, listing 13 charges against Binance and Mr Zhao.
Friends of Mr Pence claimed he is protected by the constitutional provision known as the “speech or debate.”
This follows a disclosure by his attorneys of having found a small number of classified documents at the home of the former vice president last month.
The Department of Justice is still looking into the situation, and its findings will determine how the matter proceeds.
The lawsuit asks a judge to appoint a special master to review the materials seized by the government.
Mr Giuliani also accused the officials of a “cover-up” of supposed crimes linked to President Joe Biden, without elaborating.
The WikiLeaks founder is appealing against a decision to extradite him to the United States to face spying charges.
Bitfinex said it would work with the Justice Department to regain possession of the stolen bitcoin.
Sobanke Idris Sunday Adereti, 24, pleaded guilty to false use of a passport and attempted bank fraud today before U.S. Magistrate Judge Kimberly Priest Johnson.