"You saw what Secretary Esper announced on Friday, we are putting additional forces in the region for the goal of deterrence and defense", he said.
The official did not say whether Britain believed the attack was launched from Iranian soil.
The extra US presence is the first step in increasing security, Defense Secretary Mark Esper told reporters; he didn't rule out additional moves down the road.
The Trump administration announced Friday that it would send additional US troops and missile defence equipment to Saudi Arabia and the United Arab Emirates as part of a "defensive" deployment.
While Houthi rebels claimed responsibility and Iran denied involvement, the Saudis displayed drone and missile debris as "undeniable" evidence of Iranian involvement.
Rouhani called on the foreign powers in the Persian Gulf region to "stay away".
Setting the stage for President Donald Trump's address to the annual U.N. General Assembly Tuesday, Secretary of State Mike Pompeo put aside threats of USA military retaliation against Iran for the attack.
'And we will be working with our American friends and our European friends to construct a response that tries to deescalate tensions in the Gulf region'.
Trump pulled the United States out of a 2015 nuclear deal with Iran previous year and ramped up sanctions to strangle its oil exports, a mainstay of the Iranian economy.
Trump didn't rule out meeting with Iran at the United Nations meetings in NY starting on September 23.
"What we want is that these events and actions are documented and then the global community will be within its right to ask for explanations. The priority subject is whether we can restart a de-escalation path with the different actors", Le Drian told reporters.
Iranian Foreign Minister Mohammad Javad Zarif, who is in NY for the U.N. meetings, has warned that any retaliatory strike on Iran by the United States or Saudi Arabia will result in "an all-out war".
The British foreign secretary, Dominic Raab, on Sunday described it as "implausible" that the Saudi oilfield attacks were perpetrated by the Houthi movement.
The attacks in Saudi Arabia have deepened a crisis that has escalated since US President Donald Trump withdrew from the a multilateral nuclear deal signed in 2015 between Iran and world powers.
Numerous sanctions had applied before Tehran's 2015 nuclear deal with world powers promised to lift them, in exchange for curbing the country's atomic program.