Jasim al-Khurafi, parliament speaker, told reporters of the decision at the end of a meeting with senior legislators over a cabinet request to discuss deposing the amir, as well as a letter from the amir asking for his swearing-in ceremony to be brought forward to Monday.
The move by parliament will be an unprecedented attempt to settle the constitutional crisis that has engulfed the oil-rich Western ally since the late amir, Shaikh Jabir al-Ahmad al-Jabir Al Sabah, died on 15 January and was succeeded automatically by his cousin, Shaikh Saad al-Abdulla Al Sabah.
Al-Khurafi said he had told the amir that it was too late to bring forward the oath-taking ceremony as invitations had already gone out for it to be held on Tuesday evening.
The speaker confirmed the oath-taking session was still scheduled for late Tuesday, but he said there is "a big chance that the evening session will be cancelled".
Kuwait's cabinet had asked parliament to hold a special session on Tuesday to vote on whether the new amir, who is 76 and largely incapacitated by illness, is fit to rule.
The cabinet is led by Shaikh Sabah al-Ahmad Al Sabah, the prime minister, who is the most likely contender for the post of amir if Shaikh Saad is relieved of his duties.
He is also the late amir's brother and has been de facto ruler for the past four years.
Shaikh Sabah has been de facto
ruler for the past four years
The crisis centres on the principle of alternating power between the two rival branches of the ruling Al Sabah family.
Shaikh Sabah is from the Jabir branch of the family, as was the late amir. Shaikh Saad is from the Salem branch.
Under Kuwait's succession tradition, leadership of the country has to alternate between the two branches.
Al-Khurafi said on Sunday that he was hoping that the royal family would resolve the crisis itself.