Haiti’s ambassador to the US, Bocchit Edmond, said there was “no way” US drugs agents carried out the attack. He believed it was the work of “professional mercenaries”.
Mr Edmond later told Reuters news agency that the attackers were masquerading as US drug agents when they entered the president’s residence.
Addressing the nation, Mr Joseph vowed the killers would be brought to justice and said the security situation was “under control”.
There has been widespread international condemnation of the assassination. The UN Security Council, which is due to hold a closed-door meeting on the killing on Thursday, issued a statement in which it made “an emphatic call on all political stakeholders in Haiti to refrain from any acts of violence or incitement”.
Who will take control?
Mr Joseph said that “all measures have been taken to ensure continuity” and that “democracy and the republic will win”.
But questions remain about how much control he can assert.
Haiti’s constitution says ministers, under the leadership of the prime minister, take control in the event of presidential vacancy until elections can be called.
But that also remains unclear, as a new prime minister, Ariel Henry, was named by Mr Moïse just this week but has yet to be sworn in.
The US said it believed elections should go ahead this year, to bring about a peaceful transfer of power.
Ruling by decree
Jovenel Moïse’s time in office was rocky, as he faced accusations of corruption and there were widespread demonstrations in the capital and other cities earlier this year.
Parliamentary elections should have been held in October 2019 but disputes have delayed them, meaning Mr Moïse had been ruling by decree.
In February this year, on the day the opposition wanted him to leave office, Mr Moïse said an attempt to kill him and overthrow the government had been foiled.
Haiti has also faced a wave of gang violence and kidnappings, particularly in the capital, with a number of its districts becoming no-go areas.
The worsening living standards in the nation of 11 million people have pushed nearly 60% below the poverty line.
An earthquake in 2010 killed more than 200,000 people and caused extensive damage to the infrastructure and the economy.
A UN peacekeeping force was put in place in 2004 to help stabilise the country, and only withdrew in 2017, but the turmoil has shown no sign of ending.