The U.S. leader said he did not want to act hastily. The comparison to 9/11 was notable because 15 of the 19 hijackers who deliberately crashed four planes that day were Saudi nationals.
The attack occurred this weekend and targeted Saudi Aramco facilities in Abqaiq and Khurais.
Oil prices slid on Tuesday, although the market remains on tenterhooks over the threat of a military response to attacks on Saudi Arabian crude oil facilities that halved the kingdom's output and prompted a price spike not seen in decades.
However, the USA has instead suggested that Iran was behind the operation, alleging the refineries were hit by a combination of drones and cruise missiles launched from the north of the impact site, rather than Houthi positions in Yemen to the south. US officials also said there were 19 impact points at the site, the BBC noted.
Khamenei said the US wants to prove its "maximum pressure policy" against Iran is successful.
It there is, as Washington claims, "no evidence" that the attacks were launched from Yemen, one could, with equal if not greater justification, observe that there is likewise "no evidence" that they were not launched by the U.S. itself, or by its principal regional ally, Israel.
The threat of a United States assault on Iran paving the way to a third world war must be answered through a politically conscious and independent intervention of the working class to put an end to imperialism and reorganize society on socialist foundations.
US officials say they believe that the attacks came from the opposite direction, possibly from Iran itself rather than Yemen, and may have involved cruise missiles. In this way the U.S. may become the main beneficiary of Saudi oil troubles.
The attacks have raised questions about how the kingdom, one of the world's top spenders on weaponry, much of it supplied by USA companies, was unable to protect oil plants from attack.
The market eased from its peak after Trump said he would release USA emergency supplies and producers said there were enough stocks stored up worldwide to make up for the shortfall.
While the world was still grappling with the after-effects, one expert said there was one thing that he found most shocking about the drone-powered strike, which effectively wiped out half of the country's output.
But she did leave open the door to a potential meeting between Trump and Iranian President Hassan Rouhani next week in NY - something that was a possibility before the attack in Saudi Arabia.
"Saudi Arabia has to consider its own vulnerability in launching any form of retaliation against Iran", said Anthony Cordesman, from the Washington-based Center for Strategic and International Studies.
Most of the new oil produced in the U.S.is light and sweet. "These attacks resulted in production suspension of 5.7 million barrels of crude oil per day", Saudi Aramco said in a statement.
Iranian President Hassan Rouhani said the strikes were carried out by "Yemeni people" retaliating for attacks by a Saudi-led military coalition in a war with the Houthi movement.
"What got hit is really important and serious, and this is not going to be a "We're fixing it in two days" kind of thing", said Amy Myers Jaffe, senior fellow at the Council for Foreign Relations.
North Atlantic Treaty Organisation chief Jens Stoltenberg told AFP in Baghdad on Monday that he was "extremely concerned" about escalating tensions following the attacks, and accused Iran of "destabilising" the region.