Haiti currently has neither a president nor parliament and, according to its constitution, only the latter can sack a sitting prime minister.
Conille was sworn in on 3 June.
"This resolution, taken outside any legal and constitutional framework, raises serious concerns about its legitimacy," Conille's letter was quoted as saying.
Haiti's transitional presidential council (TPC) was created in April after Ariel Henry, Conille's predecessor, was forced from office by a network of gangs that had taken over parts of the capital Port-au-Prince.
Henry left Haiti to attend a summit in Guyana on 25 February 2024 and gang members subsequently seized the city's international airport, preventing him from returning.
The TPC was tasked with restoring democratic order to the Caribbean country, where such violence is rife.
More than 3,600 people have been killed in Haiti since January and more than 500,000 have had to leave their homes, according to the UN, which describes Haiti as being one of the poorest countries in the world.
Two million Haitians currently face emergency levels of hunger, UN data shows, while almost half the population "do not have enough to eat".
One of the country's most powerful gang leaders, Jimmy Chérizier, also known as Barbecue, previously said he would be prepared to end the violence if armed groups were allowed to be involved in talks to establish a new government.
Presidential elections were last held in Haiti eight years ago, when Jovenel Moïse of the Tèt Kale party was elected.
Since his murder in July 2021, the post of president has been vacant.
Gangs in Haiti have capitalised on the power vacuum and expanded their control over swathes of the country, which has effectively been rendered lawless in places.
Last month, it was reported that hundreds of police officers had been deployed to Haiti from Kenya, with more set to join them in November.
Source: BBC
