Senators have unanimously urged Attorney-General Christian Porter to develop a new protocol for search warrants after federal police were forced to hand back emails seized in a raid.

The Australian Federal Police were last week ordered to give up material, relating to Home Affairs Minister Peter Dutton granting visas to European nannies, recovered in a raid on his department.

On Thursday, the Senate passed a motion calling on Mr Porter to urgently develop new protocols to address AFP and other executive agencies breaching parliamentary privilege.

The upper house's powerful privilege committee will also force the AFP to explain why they are not in contempt of parliament over the controversial raid.

Under parliamentary privilege laws, warrants should not be executed which interfere with the functioning of parliament.

A finding of contempt can be punished with fines and up to six months imprisonment.