Yemen's army said early on Saturday it had responded against Houthi forces on several fronts along the lines of contact.
The army did not give details of the operations or say when they took place, but said it would respond to any further targeting of its units with what it called necessary military measures.
The exchanges mark a sharp escalation between the Houthis and forces of Yemen's internationally recognised government after years in which large-scale fighting between the two sides had largely subsided, raising fears of a return to a broader conflict.
With the US-Israeli war on Iran expanding to much of the region, a senior Saudi official said on Thursday Riyadh expected imminent co-ordinated attacks from Yemen's Houthis as well as Iraqi militias under the supervision of Iran's Islamic Revolutionary Guard Corps.
Iran and its allies in Yemen and Iraq have not responded to the Saudi claim.
The Houthis said on Friday they had targeted Saudi-backed forces, depots, vehicles and military equipment at Yemen's Sahn al-Jinn camp in Marib with missiles and drones.
Reuters could not independently verify the claims by either side.
The attacks came a day after at least 30 Yemeni government troops were killed in strikes on military camps in Marib and Hadramawt provinces, according to government sources, in one of the deadliest escalations in months.
The Houthis also claimed responsibility for Thursday's attacks, saying they struck Saudi military deployments in the two provinces after detecting what they described as a large Saudi military build-up ahead of an escalation against areas under their control.
United Nations Special Envoy for Yemen Hans Grundberg said on Friday the latest attacks in Marib and Hadramawt, together with renewed attacks on commercial shipping in the Red Sea and Gulf of Aden, had left Yemen at its greatest risk of renewed large-scale conflict since the UN-brokered truce in April 2022.
He urged all sides to exercise maximum restraint and engage in UN-led negotiations, warning the violence risked drawing Yemen deeper into a wider regional confrontation.
The UN Security Council also expressed concern on Friday at the heightened tensions in Yemen, saying recent actions threatened regional security and navigational rights and freedoms, risked further escalation and undermined efforts to secure peace.
It urged the Houthis to refrain from escalation and encouraged the "use of existing channels of dialogue" to reduce tensions.
The Houthis declared a naval blockade on Saudi Arabia in the Red Sea in July in response to what they described as a Saudi siege of Yemen, an allegation Riyadh denies.
Saudi Arabia has led a military coalition backing Yemen's internationally recognised government since 2015, after the Houthis seized the capital, Sanaa, in 2014.
The war has devastated Yemen and triggered one of the world's worst humanitarian crises.
The 2022 truce had halted offensive military operations inside Yemen and across its borders and led to a sharp reduction in fighting.
The truce was twice extended before formally expiring in October 2022, but large-scale hostilities did not immediately resume and Yemen entered a period of relative calm.
