President Michel Martelly, in a speech Friday night, urged calm, The Miami Herald reported.
"I regret that it's at this moment when the country is taking off," Martelly said of Conille's decision.
Martelly, a popular singer, was elected president last year. Conille, who was a U.N. development specialist and chief of staff to U.S. President Bill Clinton in his capacity as special envoy to Haiti, was in office for only four months after Martelly's first two choices were rejected by Parliament.
The relationship between the two men had deteriorated, The New York Times reported. Observers said the breach became open a few weeks ago when Martelly interrupted a meeting between Conille and members of Parliament to accuse them of conniving against him.
Conille's resignation could threaten foreign aid for relief from last year's devastating earthquake.