Yemeni government forces launched attacks on the Houthis from three fronts in the north, west, and south of Yemen, according to military sources.
Additionally, Yemen's armed forces said they have begun a "strategic offensive" in Yemen's capital, Sanaa.
The Iran-aligned Houthis have held the capital and vast parts of the northwest, where most of the population lives.
Saudi-led coalition provides cover for Yemen's gov't forces
The Saudi-led coalition said that it is providing air cover for Yemeni armed forces on the ground, with 100 fighter jets reported to have taken part in the operation.
The coalition says it attacked 324 "high-value targets" and is providing air support at the Bab el-Mandeb Strait in the Red Sea.
Houthi-run body warns airlines flying in Saudi airspace
Yemen's Houthi-run maritime coordination body issued a warning on Monday for airlines flying in Saudi airspace, Houthi-affiliated media reported, as Saudi-backed government forces launched major offensive against the Iran-aligned group.
The maritime coordination body said the kingdom's airspace would not be safe as long as Saudi's "aggression" continued.
The Saudi government media office didn't immediately reply when asked about the warning.