Yemen's al-Masirah television network reported on Wednesday that the Saudi soldiers were killed by snipers of the popular Houthi Ansarullah movement during Yemeni operations in the Najran region.
A large number of Saudi forces and mercenaries were also injured in the Yemeni attack.
Earlier in the day, the Yemeni military announced that at least 82 Saudi forces were killed and 41 injured in the Saudi provinces of Jizan, Najran and Assir in April.
It also said that 55 were killed and 53 wounded in March.
Meanwhile, the Ansarullah movement announced that it would be increasing its strikes on Saudi Arabia’s oil facilities in retaliation for the kingdom’s war on its impoverished neighbor.
Mohammad al-Bukhaiti, a top figure in the movement’s Supreme Political Council, told The Financial Times that the fighters were manufacturing their own missiles, dismissing Riyadh's accusation that Iran was delivering the projectiles to the fighters.
On Saturday, the Houthis fired eight missiles at a number of “economic and vital targets” in the southwestern Saudi region of Jizan. Yemen’s Arabic-language al-Masirah television network cited a military source as saying that the projectiles hit their targets with great precision.
Bukhaiti said the counterattack “was only the beginning of the response” to the killing of Saleh al-Samad, the head of the Supreme Political Council assassinated by Saudi forces last week.
So far, the Houthis have successfully hit facilities belonging to the Saudi state oil giant on many occasions.
Yemen’s defenseless people have been under massive attacks by the coalition for almost three years but Riyadh has reached none of its objectives in Yemen so far.
Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to fugitive former president Abd Rabbuh Mansour Hadi.
Over 14,000 Yemenis, including thousands of women and children, have lost their lives in the deadly military campaign.