The House Committees investigating Trump had scheduled Blair's dismissal for Monday.
"Mr. Blair is caught between the allegations of the legal duty of two equal government branches, a conflict he can not resolve," said Blair's lawyer Whit Ellerman CNN on Saturday.
"Given the clear direction given to him by the executive, Mr. Blair has respectfully refused to appear and testify, yet he will fulfill all his legal obligations as soon as this conflict is properly resolved."
Blair has not received a summons, but Ellerman said Blair will still refuse to testify when summoned.
"The White House and the Council of (Departmen" Blair , who previously served as Deputy Director of National Security Programs in the Office of Administration and Budget, followed Mulvaney in January as his deputy in the West Wing National Security Advisor after Mulvaney's inauguration as chief of staff.
Prior to joining the Trump administration, Blair served as a human resources director in the House subcommittee on defense.