The argument comes despite calls by Kuwait's ruler to give the new cabinet a chance just three months after another row led to the resignation of the previous line-up.
Musallam al-Barrak, a key member of the Popular Bloc opposition party, said he and two fellow parliamentarians had lost trust in the minister despite his public regret over the remarks.
"We are worried about the minister's continued stay in office in this important and vital sector that accounts for 95 per cent of the state's income," he said after submitting the request with an Islamist deputy and a legislators of the National Bloc.
He said legislators expected to question the minister on June 25.
A public questioning is parliament's sharpest weapon as it could lead to a no-confidence motion.
Deputies often threaten to question ministers to force them to resign to avoid a tough grilling in public reported extensively by media.
The move came as the cabinet was expected to discuss the matter later on Sunday, its first meeting after prime minister returned from a two-week trip to Asia.
The country's ruler, Emir Sheikh Sabah al-Ahmad Al Sabah, has called on parliament to give the new government a chance.
The emir has the last say in politics but tends only to enter the fray to resolve major issues. Kuwait's rulers have dissolved parliament several times since it was set up in 1963.
Sheikh Khalifa has denied any wrongdoing and a ministers' court dropped the case against him on a technicality in 2001.
Changes in senior personnel at the oil ministry usually do not affect Kuwait's energy policy.