Colonel Majed al-Nazili, spokesman for the Yemeni armed forces, said the military had begun a "strategic attack" on Sanaa as part of the Yemen Dawn operation.
"Our armed forces have begun carrying out a strategic attack on Sanaa," al-Nazili said in a statement, adding that "modern capabilities" were being used.
He did not specify the nature of the attack or the targets.
Rashad al-Alimi, chairman of Yemen's Presidential Leadership Council, announced the launch of the operation earlier on Monday, saying it was aimed at restoring state institutions, retaking the capital and ending Houthi control.
The offensive comes as government forces also reported advances along Yemen's western coast near the Bab el-Mandeb Strait, a strategic maritime choke point linking the Red Sea and the Gulf of Aden.
Al-Nazili said the Giants Brigades and Nation's Shield Forces had taken control of the Bab el-Mandeb region and Dhubab airport, and had cut the road linking Dhubab and Mokha.
He said hundreds of Houthi fighters were surrounded in the Dhubab area and called on them to surrender.
Yemen's Information Minister Moammar al-Eryani also told Reuters that government forces had secured effective control of the Bab el-Mandeb Strait.
The Houthi-controlled Saba news agency, however, quoted a Houthi military source as denying reports of advances towards Dhubab, calling them "untrue".
The source said the reports were an attempt to conceal what it described as the "failure and repeated defeats" of Saudi-backed forces.
Yemen's army on Monday retook control of the Red Sea port of Mocha, captured last month by the Houthis, the government said.
The developments came amid renewed fighting on several fronts as part of the "Yemen Dawn" operation announced by the Yemeni leadership on Monday.
But the Iran-aligned Houthi movement made important advances near the city of Taiz, gaining sections of a mountain road to leave government forces there besieged, five military sources with the Yemeni government told Reuters.
Saudi Arabia, which arms and trains Yemeni government forces, is backing the military campaign with air power and has sought logistical help from allies to push back the Houthis, restore free traffic in the Red Sea and end the group's attacks on its territory.
Saudi authorities said on Monday they had attacked hundreds of targets in Yemen to provide air cover for the Bab el-Mandeb Strait and Yemeni ground forces.
The rival factions in Yemen have been engaged in heavy fighting again for weeks.
In September, the Houthi militia seized control of Yemen's entire Red Sea coast in a lightning offensive, also gaining access to the strategically important strait of Bab el-Mandeb (Gate of Tears).
The importance of the Bab el-Mandeb Strait has increased further as a result of the crisis in the Strait of Hormuz.
Passage through the Strait of Hormuz has been severely restricted since the start of the war launched by the US on Iran and as Iranian authorities seek to control transit through the strait.
with Reuters
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