"The prime minister [Sheikh Nasser Mohammad al-Ahmad Al-Sabah] has submitted his resignation to the emir," Kuwait TV said, without specifying whether it had been accepted.
Earlier, opposition member Khaled al-Sultan said the cabinets's resignation was accepted amid a bitter political dispute between the prime minister and opposition MPs.
"We are waiting for the appointment of a new prime minister before parliament is dissolved in order to be assured of fair elections," the Sultan told reporters outside parliament.
Parliament speaker Jassem al-Khorafi said he had not been informed about a dissolution of parliament.
If it is confirmed that Sheikh Sabah al-Ahmad al-Sabah, the emir of Kuwait, has accepted the resignations, he may then also dissolve parliament before setting a date for new elections.
Several opposition MPs welcomed the resignation.
"I hope that the emir will please the Kuwaiti people by dissolving parliament ... and forming a transitional cabinet to supervise the elections," opposition MP Falah al-Sawwagh told reporters.
Multiple resignations
The announcement of the resignations came after the emir chaired an emergency meeting of the cabinet headed by the prime minister to discuss the political crisis.
Sheikh Nasser, 71, had been due to be questioned in parliament by three opposition MPs on allegations of fraud, including charges that he transferred public funds into his overseas accounts.
The government has denied the charges.
The move also came ahead of a planned mass rally later on Monday by the opposition to press demands for the premier's ousting.
Sheikh Nasser, a nephew of the emir, was appointed to the post in February 2006 and has since now resigned seven times because of political turmoil.
Parliament has been dissolved three times over the same period.
Unprecedented probe
The public prosecutor in September launched an unprecedented probe into the bank accounts of around 15 pro-government MPs who were accused of accepting bribes totalling $350m.
Opposition MPs have claimed the deposits were bribes by the government to win votes on crucial issues.
Some of the concerned MPs have denied any wrongdoing.
Nahaj, an alliance of opposition groups and youth organisations, insisted in a statement that the prime minister be replaced and parliament dissolved.
They also called for opposition detainees to be released. Twenty-four opposition activists are serving a three-week detention pending trial after parliament was stormed on November 16.
Kuwait, which sits on about 10 percent of global crude oil, has amassed more than $300 billion in surpluses over the past decade, but projects and development have been stalled by political wrangling.