"We were assured by the premier that the state is pursuing all channels to secure al-Kasasba's release," Senate Speaker Abdel Raouf Rawadeh was quoted as saying by Anadolu after the session.
In its latest message that could not be immediately verified, IS extended its Wednesday deadline for a prisoner swap with Jordan to late Thursday, according to numerous media reports.
Reports began to emerge on Tuesday that Jordanian authorities were considering releasing Sajida Rishawi, a female suicide bomber, in exchange for Muath Kasaesbeh and Japanese journalist Kenji Goto.
Kasaesbeh was immediately captured by the Islamic radical group militants after his plane crashed near the IS stronghold of Raqqah in Syria on December 24, 2014.
Goto allegedly went to Syria in October to negotiate the release of Haruna Yukawa, a Japanese security company executive. The IS extremists last week demanded a $200-million ransom for the two Japanese captives.
On Sunday, IS released a video showing Goto holding an image of what appeared be Yukawa's beheaded body. The radical Sunni group has become known for atrocities that include public crucifixions and beheadings of captured prisoners, including journalists.