The shake-up is the latest blow to political stability in the country, which has been wracked with worsening violence. Armed gangs have gained control of most of capital Port-au-Prince and expanded to nearby regions, fuelling hunger and forcing hundreds of thousands from their homes.
Promised international support still lags and nearby nations have deported Haitian migrants back to the country.
The resolution, dated on Monday, is expected to be published in the official gazette.
Didier Fils-Aime is the son of well-known Haitian activist, Alix Fils-Aime, who was jailed under the regime of dictator Jean-Claude "Baby Doc" Duvalier.
Conille, who also briefly led the country over a decade ago, has been prime minister for about six months. He was appointed to the role in May by Haiti's transition council to return to the role as the Caribbean nation works to restore stability.
The transition council, named in April, was tasked with choosing a prime minister and wielding certain presidential powers until conditions are considered secure enough for a new election. There has been some infighting among its councillors.
In recent weeks, Conille embarked on trips abroad to the United Arab Emirates and Kenya to seek security assistance in the aftermath of a deadly gang attack that killed at least 70 people.
In a letter circulating on social media, Conille said the transition council only had power to appoint a prime minister, but not dismiss one from the role.
"This resolution, taken outside any legal and constitutional framework, raises serious concerns about its legitimacy and its impact on the future of our country," the letter said.
A spokesperson for the prime minister's office did not respond to a request for comment.
