It followed two similar attacks, one in September against the headquarters of the national oil company that killed two and another that hit the electoral commission in Tripoli in May, when 14 were slain.
Reporting from Tripoli, Al Jazeera's Mahmoud Abdelwahid said a security official and an employee of the ministry were killed in the attack on Tuesday.
Sources in Tripoli announced that the attack was carried by several "terrorists" who broke into the Ministry's building.
Mr Siala was not injured in the attack.
Twenty-one other people were wounded in the attack claimed by Daesh.
"Turkey will maintain its solidarity with the people and the Government of Libya in the fight against terrorism", it added.
Libyan Interior Minister Ashour Suleiman Shuwail admitted there had been a security lapse, which he planned to overcome.
Plumes of smoke were seen rising from the building as ambulances, paramedics and security forces gathered outside.
Fire and rescue teams eventually brought the blaze under control, but the outside of the building was charred.
The government called on the Libyans to take caution following the attack.
Libya descended into a period of chaos after uprisings in Tunisia and Egypt led to similar protests against Qaddafi in 2011. The Tripoli government is recognized by the United Nations.
Talks have been held in recent months in Paris and Sicily to try to advance the political process in this country of some six million inhabitants, including the holding of elections.
"In the absence of a monopoly on the use of force in the country, IS has been able to consolidate", said Mohammed al-Agouri, a professor at Benghazi university in eastern Libya.
A security cordon was set up around the premises of the department ravaged by fire, before the civil protection services can overcome the fire, according to AFP journalists there.