"We heard from the emir that he was keen for democracy and the National Assembly and that it should complete its [four-year] term," Jassem al-Khorafi, the parliamentary speaker, said.
"The National Assembly will continue with its business as usual."
It would be the third time in three years that parliament has been dissolved if the emir had not taken the decision.
In May 2006 and March 2008 confrontations between MPs and government forced dissolutions of parliament.
Sheikh Nasser and cabinet members walked out of parliament on Tuesday as it was due to set a date to question the prime minister, a move that could have led to his impeachment.
Nasser al-Sane, an MP, told Al Jazeera: "We expect in the comming days that the emir will accept the resignations and reassign the prime minister to form a new cabinet."
Three Islamist MPs called for the questioning of Sheikh Nasser, a nephew of Sheikh Sabah, last week.
They accused Sheikh Nasser of allowing a prominent Iranian Shia leader to enter Kuwait despite the fact he was banned.
They have also accused him of failing to "perform his constitutional duties ... and that it was time that Kuwait had a premier capable of running the state and achieving the wishes of the people".
Additionally, the trio said that the corruption and squandering of public funds has increased under Sheikh Nasser's leadership.
The Al-Sabah family has controlled Kuwait for its complete 250-year history.