At least five air strikes hit military sites and an area near the presidential palace compound in the Yemeni capital Sanaa at dawn on Sunday while warships pounded an area near the port of the southern city of Aden, residents said.
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.
Aden residents reported heavy clashes between local armed militia and Houthi fighters backed up by army units, and sources in the militia said they were retaliating for the first time with tank and Katyusha rocket fire against the Houthi advance.
In the southern province of Dalea, the militiamen said they had fought for hours to retake several rural districts with the help of Saudi-led air strikes, in fighting which left around 25 of the Houthi forces and six of their own men dead.
Saudi Arabia, the world's top oil exporter and arch regional adversary of Iran, is concerned about possible security threats posed by the Houthis' advance across Yemen since last September.
It launched a month-long campaign of air raids against the group that has halted its battlefield progress but has yet to reverse their dominant position in the country or force them to return to peace talks.
