"The prime minister has submitted his resignation to the emir," Kuwait state-run television said, without specifying whether it had been accepted. Earlier, opposition lawmaker Khaled al-Sultan said the government'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 Islamist opposition MP told reporters outside parliament.
Parliament speaker Jassem al-Khorafi said he had not been informed about a dissolution of parliament.
The announcement came after Emir Sheikh Sabah al-Ahmad Al-Sabah chaired an emergency meeting of the cabinet headed by Prime Minister Sheikh Nasser Mohammad al-Ahmad Al-Sabah to discuss the emirate's latest political crisis.
Sheikh Nasser, 71, had been due to be questioned in parliament by three opposition MPs on allegations of graft, 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 ouster. 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.
Several opposition MPs welcomed the resignation and called for parliament to be dissolved and early elections. "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.
Independent opposition MP Mubarak al-Waalan called for the appointment of a new premier to lead the transitional government until polls are held. "We are waiting for the next step to dissolve parliament, a quarter of whose members have been referred to the prosecution" over large allegedly illegal deposits in their accounts, MP Daifalla Buramia said in a statement.
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 $350 million.
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.