Sources in Sanaa said that head of the so-called supreme political council Mahdi al-Mshat, head of the so-called revolutionary councils, Mohammed Ali al-Houthi, and other officials were in the building at the time of the attack.
Salam called on the people of Yemen to continue supporting the fronts with money and men to confront the aggression and thwart its plans.
The Houthis' Al-Masirah television channel accused the Saudi-led coalition, which has been fighting the rebels since 2015 to shore up the internationally recognised government, of responsibility for the strikes.
Witnesses cited by AP said the palace, situated in the commercial district of Tahrir, was targeted repeatedly by Saudi-led Arab coalition jets.
"We were working next door to the presidential offices and heard a plane, and then an explosion", Ahmed Dehashir, a first responder.
"Some people rushed to the scene and saw the destruction and people caught under the rubble". He also said that "There are a lot of people trapped under the rubble".
The Iranian-planned Houthi attacks, which are strongly denounced by the global community, reveal their terrorism and never affects our stability and development.
Launched from within the territory of Yemen, north of Amran governorate, the missiles were intercepted at 8.47pm, Saudi Press Agency reported. Since November 2017 Houthi Ansarullah movement has intensified missile attacks into Saudi Arabia.
Yemen's policy of targeting only Saudi Arabia's economic facilities and state-run airports and its refusal to attack civilian areas signifies that the Yemeni forces respect moral and human values, the commander explained.
The United Nations has listed Yemen as the world's number one humanitarian crisis, with seven million Yemenis on the brink of starvation and cholera causing more than 2,000 deaths.
Earlier this month Abu Dhabi had deployed some 300 soldiers, along with tanks and artillery in the island amidst widening divisions within the Riyadh supported forces loyal to Abd Rabbuh Mansour Hadi.