It quoted a military statement as saying the plane came down in Marib province, east of the capital Sanaa. "As a result, four officers and eight non-commissioned officers from the Saudi armed forces were martyred," SPA said. It gave no details on the cause of the crash, saying it was under investigation.
The death toll was one of the largest in a single incident involving Saudi forces since a coalition of Arab states began military operations against the armed Houthi movement in 2015 to try to restore Yemeni President Abd-Rabbu Mansour Hadi to power.
A ballistic missile fired by the Houthis towards a coalition military base in Marib in 2015 killed more than 60 troops from the United Arab Emirates, Saudi Arabia and Bahrain.
The Saudi-led coalition has recently made some gains against the Houthis in western Yemen , but fighting on other fronts, including Marib, has been static, with little ground changing hands.
The Houthis seized much of northern Yemen , including the capital Sanaa, in a series of military operations that began in 2014, eventually forcing Hadi to flee.
The Saudi-led coalition accuses Iran of trying to use the Houthis to expand its influence in Yemen , one of the poorest Arab countries. The Houthis regard their move on Sanaa as a revolution against corruption.