In a brief statement, Burris said, he is "not seeking to have any type of confrontation." He said he would now meet with his lawyers to decide his next step.
Timothy Wright, Burris' attorney, then addressed reporters. He said the secretary of the Senate's decision was "against the law of this land" and noted that Burris had not been allowed to proceed to the Senate floor to take the oath of office.
"There are remedies before us to right those wrongs," Wright told CNN soon after.
The Illinois secretary of state declined to sign a certificate officially nominating Burris to the seat, despite the move by embattled Illinois governor Rod Blagojevich to appoint him. State legislators are now holding hearings over impeaching Blagojevich, who has been charged with trying to effectively sell the seat, which had previously been held by President-elect Barack Obama.