The tiny west African state has been in the grip of a power struggle since August 2015.
In a unanimous statement adopted after a closed-door meeting, the council said it was ready to "take necessary measures to respond to further worsening of the situation in Guinea Bissau."
The tiny west African state has been in the grip of a power struggle since August 2015, when Vaz sacked then-premier Domingos Simoes Pereira, leader of the African Party for the Independence of Guinea and Cape Verde (PAIGC).
A new prime minister, Umaro Sissoco Embalo, was sworn in last December but PAIGC rejected him, accusing Vaz of breaching an agreement calling for a consensual choice of prime minister.
The council "invited President Vaz to appoint a prime minister whose selection respects the provisions of the Conakry agreement" that calls for a consensus candidate.
Council members said the crisis was "as a result of the inability of political stakeholders to reach a lasting and consensual solution, leading to the current gridlock".