The bombings were the first raids on Sanaa since a Saudi-led alliance said last week it was scaling back a campaign against Iranian-allied Houthi militias, which control Sanaa and have powerful allies in Yemen's factionalised armed forces.
"The explosions were so big they shook the house, waking us and our kids up. Life has really become unbearable in this city," a Sanaa resident who gave his name as Jamal told Reuters.
Eyewitnesses in Aden said foreign warships pounded Houthi armed positions around the city's main commercial port and dockyard, the first time the port area has been shelled, residents said.