Shaikh Saad al-Abdullah al-Sabah, 76, was proclaimed amir last Sunday after the death of his cousin, Amir Shaikh Jaber al-Ahmad al-Sabah, 78.
But the cabinet said on Saturday it was invoking a law that allowed it to ask a medical team to examine Shaikh Saad and report to parliament on his ability to rule. Any step to remove him would require a two-thirds vote in parliament.
The amir, however, had asked parliament to allow him to take the oath of office.
Under the constitution, he has to take the two-line oath in front of a special parliament session before he can formally assume his responsibilities as ruler.
"If His Highness the amir wishes to take the oath, we cannot reject such a request"
Jassem al-Kharafi, parliament speaker
"If His Highness the amir wishes to take the oath, we cannot reject such a request," al-Khurafi told reporters.
KUNA the state news agency announced that "[House speaker] informed His Highness that the National Assembly welcomed his request to hold a special session to take the constitutional oath". It said that the swearing-in session would be held on Tuesday.
Shaikh Sabah al-Ahmad al-Sabah, the prime minister and brother of the late amir, has been de facto ruler for the past few years, and analysts have said he would be the most likely contender for the post of amir if Shaikh Saad had to step down.
But appointing Shaikh Sabah would break with a long-held tradition of power-sharing by Kuwait's two branches of the royal family - the Jabers and the Salems. Shaikh Sabah and the late amir belong to the Jaber branch.
Shaikh Saad, from the Salem branch, had colon surgery in 1997. He was admitted in hospital last year with excessive blood glucose levels and has had treatment abroad often since then, most recently in August.
Earlier on Sunday, the cabinet indicated that it was pressing on with its insistence on a medical examination.
But several elders of the ruling family, mostly those from Jaber branch of the dynasty, met Shaikh Sabah on Friday and voiced confidence in his ability to continue to run Kuwait, an Opec producer with nearly a tenth of the world's oil reserves.
The show of support was interpreted by the local media as paving the way for him to assume the state's top post.
There are growing calls for Shaikh
Sabah to become amir
However, Nabil al-Fadl, a columnist, said in an editorial in al-Watan daily that Shaikh Saad's side of the family, the Salems, should not keep pushing for him to assume power as amir "after his health and mind had failed according to God's will".
State television had shown a frail-looking Shaikh Saad, wheelchair-bound, receiving condolences two days after the late amir died. Shaikh Saad's public appearances have been rare in recent years.
The struggle over the succession has caused some confusion in the US-allied Gulf Arab state.
The stock market fell on Saturday but recouped some of its losses on Sunday.
Shortly after al-Khurafi spoke, workers put up pictures of Shaikh Saad with a Kuwaiti flag behind parliament's outer wall.