The violence came a day after the UN declared its highest level of humanitarian emergency in the country, where it says some 3,000 people, half of them civilians, have been killed since March.
But there was a ray of hope, as the Red Cross said it had begun distributing food in the beleaguered city of Aden, where it said around half the people are displaced from their homes.
The clashes in Aden erupted at dawn in northern part of the port city, killing seven rebels and five pro-government fighters, a military official said.
The bloodshed comes a day after rebel rocket fire hit a residential district of Aden, killing 31 civilians and wounding more than 100.
Meanwhile, a port near the oil refinery came under rebel artillery fire for a fifth consecutive day, as a fire continued in the area, said Aden Refinery Co. Spokesman Naser al-Shayef.
In Sanaa, warplanes pounded several positions of the Huthi rebels around midday, residents reported.
Medical officials said eight rebels were killed and at least 10 wounded in the strikes, which they described as the most violent since the Muslim fasting month of Ramadan began two weeks ago.
Amnesty International warned of "the high price civilians continue to pay amid the... Air strikes all over the country" and accused the coalition of failing to "abide by the requirements of international humanitarian law".
That requires belligerents to "take all possible steps to prevent or minimise civilian casualties," said Donatella Rovera, senior crisis response adviser at Amnesty.
But there is "no indication" the coalition has done "anything to prevent and redress such violations," said Rovera, who is currently in Yemen.
