A power struggle is brewing in Haiti as the man appointed prime minister shortly before the assassination of Haiti's president this week said he - not the acting premier - should lead the Caribbean nation and was forming a government to that effect.

Ariel Henry, a neurosurgeon who was named prime minister by President Jovenel Moise on Monday, two days before Moise was killed by a squad of gunmen in his home in the capital, Port-au-Prince, said he was now the highest authority in Haiti, not interim Prime Minister Claude Joseph.

"After the president's assassination, I became the highest, legal and regular authority because there was a decree nominating me," Henry told Reuters in a phone interview late on Friday.

Henry had not been sworn in to replace Joseph at the time of the assassination, which has created confusion over who is the legitimate leader of the 11 million people in Haiti, which shares the island of Hispaniola with the Dominican Republic.

Joseph, who was named interim prime minister in April after the resignation of Joseph Jouthe, has taken the reins of power so far, spearheading the government's response to the assassination, appealing to the United States for support and declaring a 15-day state of emergency.

Elections Minister Mathias Pierre said Joseph would keep that role until presidential and legislative elections are held on Sept. 26.

Henry said the new government he was forming, however, would instead create a new electoral council - given the previous one had been considered too partisan - and the council would determine new dates for elections.

"I don't know what date they will be, all I know is that we cannot take too long to do these elections. We need to do them as soon as possible," Henry said.

Haiti's Senate, which currently comprises just a third of its usual 30 senators, nominated its head Joseph Lambert on Friday to be interim president, a document reviewed by Reuters showed.

Henry said he would be "ready to lead the country with all those who wanted to move forward" when asked if he was willing to rule alongside Lambert.

(With input from agencies)