A group of unidentified individuals attacked the private resident of Moise on Wednesday night and shot him dead, Joseph said.
The first lady was hospitalized in the attack.
“The security situation in the country is under the control of the Haitian National Police and the Haitian Armed Forces,” Joseph said in a statement from his office. “Democracy and the republic will win. “
“All measures are taken to guarantee the continuity of the state and protect the nation,” Joseph added.
Moise had ruled Haiti, the poorest country in the Americas, by decree after legislative elections scheduled for 2018 were delayed and following disputes over the end of his own term.
In the early hours of Wednesday, the streets were largely empty in Port-au-Prince, the capital of the Caribbean nation, but some people trashed businesses in one neighborhood. After the attack, gunshots were heard throughout the capital.
Joseph said police have been deployed to the National Palace and the upscale community of Pétionville and will be dispatched to other areas.
Joseph condemned the assassination as a “heinous, inhuman and barbaric act”. He said some of the attackers spoke in Spanish but offered no further explanation.
The nation of over 11 million people had grown increasingly unstable and discontented under Moses, who was 53 years old.
The attack came amid a growing wave of politically linked violence in the impoverished Caribbean nation. With Haiti politically divided and facing a growing humanitarian crisis and food shortages, there are fears of widespread disorder.
Port-au-Prince has seen an increase in violence as gangs clash and police for control of the streets.
This violence has been fueled by increased poverty and political instability.
Some 60 percent of the population earns less than $ 2 a day. These problems come as Haiti is still trying to recover from the devastating earthquake of 2010 and Hurricane Matthew that struck in 2016.
Moise has faced fierce protests since taking office as president in 2017, with the opposition this year accusing him of seeking to install a dictatorship by extending his term and becoming more authoritarian – accusations he denied.
In addition to presidential, legislative and local elections, Haiti was due to hold a constitutional referendum in September after being postponed twice due to the coronavirus pandemic.