Coalition fighter jets carried out dozens of airstrikes, according to both sides of the conflict, bombing Houthi positions inside Sanaa and in other northern provinces.
The coalition bombed Saleh’s residence and other houses of his family members, Yemen’s pro-Houthi al-Masirah television station said.
Meanwhile, residents said loud explosions were heard in downtown Sanaa.
Air raids also struck northern provinces including Taiz, Haja, Midi and Saada, the rebel-owned channel said, although there was no immediate word on casualties.
On Monday, Houthis killed Saleh, a former ally, and moved to consolidate their grip on Sanaa after day of clashes.
At least 234 people have been killed and 400 wounded in five days of heavy fighting in the Yemeni capital, according to the International Committee of the Red Cross.
On Tuesday, US Defence Secretary Jim Mattis said the killing of Saleh would short term, likely worsen an already dire humanitarian situation in the country.
The killing could either push the conflict towards UN peace negotiations or make it an “even more vicious war,” Mattis told reporters.
"(But) one thing I think I can say with a lot of concern and probably likelihood is that the situation for the innocent people there, the humanitarian side, is most likely to (get) worse in the short term,” Mattis said.
“So this is where we’ve all got to roll up our sleeves. Now, what are you going to do about medicine and food and clean water and cholera,” he added.
“I think there has got to be a lot more focus on the humanitarian side right now.”
The Houthis, who have now disassociated from forces loyal to the former president, are fighting government forces backed by a Saudi-led Arab military coalition.
More than 10,000 people – over half of them civilians – have been killed since the coalition intervened in 2015.
The fighting has caused a humanitarian catastrophe which the UN says is the world's worst, pushing seven million people to the brink of famine and sparking a cholera outbreak that the World Health Organisation says has killed 2,000 people.