"This brings the total production cut that will be carried out by the Kingdom, to around 4.8 million barrels per day, from the April production level," the official said.
"Therefore, the Kingdom's production for June, after both its targeted and voluntary cuts, will be 7.492 million barrels per day," he added.
Brent crude was up 19 cents, or almost 1%, at $31.16 a barrel by 1216 GMT, while U.S. West Texas Intermediate crude rose 38 cents, or 1.5%, to $25.12. Both contracts had fallen more than $1 earlier in the session.
Global oil demand has slumped by about 30% as the coronavirus pandemic has curtailed movement across the world, building up inventories globally.
OPEC and allies led by Russia, a group known as OPEC+, agreed last month reduce output by about 9.7 million barrels per day (bpd) for May and June, a record production cut. Producers will slowly relax curbs after June, although reductions in supply will stay in place until April 2022.
Under the deal, Saudi Arabia's targeted oil production is 8.492 million bpd in May and June.
The ministry has also directed Aramco to reduce its production in May from its quota level of 8.492 million bpd "in consent with its customers", the official said.
"The Kingdom aims through this additional cut to encourage OPEC+ participants, as well as other producing countries, to comply with the production cuts they have committed to, and to provide additional voluntary cuts, in an effort to support the stability of global oil markets," the Saudi official said.