Reuters reports, citing sources familiar with the kingdom's policy
The report says that Saudi Arabia's oil production may edge up in June but the extra crude may be used for domestic power generation rather than for export purposes, which the US has been seeking them to do in light of the situation in Iran.
The sources cited also say that any rise in Saudi oil production will still be within its OPEC+ output quota of 10.3 million bpd. As it stands, the kingdom is expected to produce around 10.0 million bpd in May itself so the nudge higher isn't likely to be of much significance.
But at least it goes to show that they are seen to be responding to US pressures, though not in the manner that the US would have hoped for just yet.