Qatari energy minister, Abd Allah al-Atiyaa, promised that Opec members would supply "as much as the market can absorb".
And Kuwait's energy minister said his country had already increased production and would lift output further if necessary.
"We have additional production capacity that we can use. We are talking about 200,000 barrels per day," said Shaikh Ahmad al-Sabah.
But US oil prices surged more than 2% to push once more above $40.80 a barrel on Tuesday.
However, analysts doubt it will beat the 21-year peak this month at $41.85 a barrel, despite the Khobar attack serving as a sharp reminder of the vulnerability of already stretched global supplies.
"This is a knee-jerk response to the weekend's events, but
I expect fundamentals to reassert themselves," said David
Thurtell of Commonwealth Bank of Australia.
Daniel Yergin, chairman of Cambridge Energy Research Associates, agreed, saying concern over supply was mostly a "psychological shock" and not a physical slump in supply.
A pipeline attack in Saudi could
cost the world dear
He added that the physical fundamentals were beginning to improve as production increased.
Nevertheless, the attacks - the second in recent weeks – have added to worries about the stability of oil supplies.
An offical at Opec, which controls 38% of the world's oil supplies, voiced his concern about instability in the kingdom, while the UK's ambassador there warned that more attacks may be imminent.
Umar Ibrahim, head of Opec's information department, said the group was "concerned about global security and stability ... and especially about security in our member countries, including Saudi Arabia and Iraq."
Any price increase, however, is likely to be dampened by the fact that the markets have had the three-day holiday weekend to digest the news of the attacks in Khobar.