Saudi Aramco has told some clients that vessel loading has resumed following disruptions caused by the weekend's attacks on Saudi oil facilities, two sources who received the notice told Reuters on Monday.
The state company's Oil Supply Planning and Scheduling (OSPAS) department said loading operations were in progress, they said, citing the notice.
Three sources with major Asian refineries, including one of the two that have seen the port notice, told Reuters their oil tanker loading was normal as of Monday.
"We have a few cargoes to load ... We are concerned about the impact (of the attack), but so far we hear from port agents that it has been OK," one of the sources said.
"Our oil loading has not been impacted yet," another one of the sources said.
"But we need to see the official notice from them (Aramco) ... It will take a bit more time to see the impact."
The sources declined to be identified as they were not authorised to speak to the media.
The attacks knocked down 5.7 million barrels per day of crude production - more than half of top exporter Saudi Arabia's output, or over 5% of global oil supply. Saudi officials have given no timeline for restoring full supply.
Saudi Arabia's return to full supply capacity after Saturday's attacks could take "weeks, not days", a source close to the matter told Reuters on Sunday.
Oil prices surged as much as 19% in early Asian trade on Monday on worries over global supply and tensions in the Middle East.