Twenty-two senators and 92 deputies were present Thursday to open the troubled country's National Assembly.
The matter of the presidential vacuum was listed on their agenda but they closed the brief session without formally discussing it. President Michel Martelly is constitutionally required to leave office Sunday.
Sen. Francois Anick Joseph said: "We hope we can find a solution by Sunday."
The two legislative leaders departed without taking questions.
A presidential runoff has been indefinitely postponed amid violent protests and suspicions of electoral fraud.
Officials are focused on finding an interim leader to head a caretaker government until voters can elect their next leader.