It also approved his decision to declare a 90-day state of emergency in the tiny West African state.
The Gambia was plunged into crisis after Mr Jammeh rejected Mr Barrow's shock victory in the 1 December election.
In his televised announcement on Tuesday, Mr Jammeh said “any acts of disobedience to the laws of The Gambia, incitement of violence and acts intended to disturb public order and peace” were banned under the state of emergency.
He said security forces were instructed to “maintain absolute peace, law and order”.
The parliament passed a motion condemning what it called the “unlawful and malicious interference” of the African Union and neighbouring countries.
Regional leaders have threatened to use military force to oust Mr Jammeh if he refuses to hand power to President-elect Adama Barrow on Thursday.
Regional bloc Ecowas, the Economic Community of West African States, has prepared a Senegal-led force but maintains that military intervention would be a last resort.