Prime Minister Elyes Fakhfakh was sworn in in February after winning a confidence vote in parliament following four months of post-election deadlock amid tensions with Ennahdha.
Fakhfakh is under investigation over alleged failure to hand over control of shares he owns in private companies that have won public contracts.
Ennahdha consultative council asked party leader Rached Ghannouchi "to carry out consultations... on a change of government", council president Abdelkarim Harouni said.
"The economic and social situation is very serious and can only be overcome by a government whose head is not suspected of any conflict of interest," he told a news conference.
"Ennahdha does not allow any suspicion of corruption to prevail in the government," Harouni said.
Relations between Ennahdha and Fakhfakh have been strained ever since the October legislative elections.
President Saied rejected Ennahdha's call for consultations to go ahead.
"There will be no consultations so long as the prime minister remains in power," his office said in a statement after a meeting with the premier.
Tunisia's already fragile economy has been battered by the coronavirus pandemic.
Fakhfakh said last month that the economy would shrink by some six percent this year as "all state enterprises are in bankruptcy".