The coalition closed all air, land and sea ports to stem the flow of weapons to Houthi rebels in Yemen after an Iranian-supplied ballistic missile was launched at Riyadh from Houthi-held territory on November 4.
Two air strikes targeted the ministry late on Friday and plumes of smoke could be seen billowing from the building, the rebel media network Al Masirah quoted witnesses as saying. There was no word of any casualties.
Saudi Arabia has blamed Iran for supplying the rebels with the missile, sparking tensions between the Middle East rivals and fears of a military confrontation.
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Al-Hamini further pointed to the brutal attacks by the Saudi-led coalition against Yemen's defenseless people and said that Yemenis believe that "firing missile at the aggressors is their right".
On Thursday, the Houthis rejected the US allegations, saying they built the missile themselves and fired it in response to coalition bombings that have killed civilians and the ongoing blockade.
The United Nations and several humanitarian groups this week warned that millions could die in Yemen from starvation if the blockade, which includes relief aid, was not lifted.
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According to the United Nations, from March 2015 to March 2017, 16,200 people have been killed in Yemen, including 10,000 civilians.
The Huthis continue to control the capital Sanaa and much of Yemen's north.
Commercial flights in and out of Yemen will resume on Sunday after the Saudi-led coalition fighting to restore the legitimate government lifted a week-long ban.
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Temperatures will remain consistent through Tuesday and Wednesday as both have a high of 46 degrees with a high of 46 degrees. Temperatures climb during the day Saturday but will remain well below-normal under mostly sunny skies, forecasts show .
"The continued closure of borders will only bring additional hardship and deprivation with deadly consequences to an entire population suffering from a conflict that it is not of their own making", they added.