According to the Al Masirah television channel, which is owned by Yemen's rebel Houthi government, the troops were killed in cross border fire at military bases inside Saudi Arabia, in Sharjah and Tal'a.
The official Saudi press agency released a report on Sunday that appeared to contradict the claims, saying just one soldier had been killed by Yemeni sniper fire.
More than 6,800 people have been killed and 35,000 injured in Yemen since March 2015, when a Saudi-led multinational coalition began to attack Houthi insurgents who had seized control of the country.
Alarmed by the rise of a group they believed to be backed militarily by regional Shia power Iran, Saudi Arabia and eight other mostly Sunni Arab states began an air campaign aimed at restoring the former government.
The conflict and a blockade imposed by the coalition — which has received logistical and intelligence support, as well as weapons, from the UK, US, and France — has triggered a humanitarian disaster in the country, leaving 80 per cent of the population in need of aid.
Yemeni armed forces said on Saturday they also launched rocket attacks at positions of Saudi-backed mercenaries near the Khadra border crossing in Najran, killing and wounding a number of them.
Army troops and allied forces also claim to have attacked the Saudi bases of Samnah and Afra in the kingdom’s southwestern province of Jizan on Saturday night, leaving an unspecified number of military personnel there dead and injured.
According to the report, Yemeni explosives also hit the Saudi army’s weapons warehouses to the west of Qais Mountain in Jizan.
The military described the attacks as retaliation for Riyadh’s nonstop military campaign against its impoverished neighbour.
It recently emerged the Saudi army had used British-made cluster bombs, which are banned by 120 countries including the UK because of the risk they pose to civilians, in Yemen. Even prior to this, the Gulf state had come under repeated criticism for its excessive use of force and neglect for the well-being of civilians in the country.
In a statement, Human Rights Watch censured Saudi-led forces for the use of cluster bombs during the “unlawful” campaign against Yemen.
The New York-based rights body said “cluster munitions are prohibited weapons that should never be used under any circumstances due to the harm inflicted on civilians.”
Yemen said it wanted the UN to intervene to end the conflict.
Yemen's splendid isolation
In a statement on Sunday, the Yemeni Human Rights Ministry condemned the Saudi regime for "war crimes", particularly its use of internationally-banned weapons against civilians.
The statement further called on the United Nations to adopt measures aimed at putting an end to Saudi brutalities, saying the world body should launch an “unbiased” investigation into the deadly Saudi-led offensive.
The ministry also urged the removal of Riyadh’s blockade against Yemen as well as swift aid delivery to the violence-stricken civilians.