"The president was speaking in his usual personal capacity, contrary to the rules and regulations, as he is not mandated to sack the prime minister of the transitional federal government," Hussein said after Yusuf announced his decision.
Under the transitional federal charter, the president needs the parliament's approval to sack the prime minister.
"The government of Nur Hassan Hussein was unable to perform its duties and I am obliged to save the country"
Abdullahi Yusuf Ahmed,
But Yusuf expressed confidence that MPs would back his decision.
"Most of the parliamentarians will endorse my decision to dismiss the prime minister," he said.
"Should parliament reject my desire to look for a new prime minister, I will comply with their decision and the current government will continue its tenure."
Dr Yusuf al-Hazari, a political and legal adviser to the president, told Al Jazeera that Yusuf had the right to remove the prime minister if he failed to form a cabinet within the time limit set by the constitution.
"That is always one month and he couldn't establish or form the cabinet ... Nur Hussein could not compose it in two months and 16 days," he said.
Last month, Hussein blamed the president, who has been head of state since the inception of the transitional government in 2004, for the problems in the government due to his refusal to approve new ministers.
Leaders in the Inter-Governmental Authority on Development (IGAD), made up of Ethiopia, Djibouti, Kenya, Sudan, Uganda and Somalia, had called for the new cabinet to be named at a meeting in October.
Hussein replaced Ali Mohamed Gedi who was forced to resign after months of a struggles with Yusuf.
In 2008, he survived a vote of no confidence after some legislators accused him of embezzling state funds.
The transitional government in Somalia has struggled to enforce its control over the chaotic country and in 2006 needed assistance from the Ethiopian military to retake large areas of the country controlled by the Islamic Courts Union.
Since then government forces and their Ethiopian allies have come under near daily attack as the oppostion fighters have gradually re-established their influence.
In November, Yusuf said the government was "on the verge of total collapse" after opposition fighters retook control of large areas of the country.