A US official said that there were 19 points of impact on the targets and the attacks had come from a west-north-west direction, not Houthi-controlled territory in Yemen, which lies to the south-west of the Saudi oil facilities, reports the BBC.
Other American officials said that could suggest launch sites in the northern Gulf, Iran or Iraq.
A close-up image of damaged tanks at the Abqaiq processing plant appeared to show impact points on the western side.
Officials quoted by the New York Times said a mix of drones and cruise missiles might have been deployed, but that not all hit their targets at Abqaiq and the Khurais oilfield.
ABC quoted a senior US official as saying that President Donald Trump was fully aware that Iran was responsible.
The attacks on Saturday was carried out by 10 unmanned aircraft. It hit the Hijra Khurais - one of Saudi Arabia's largest oil fields, producing about 1.5 million barrels a day - and Abqaiq, the world's biggest crude stabilization facility, which processes seven million barrels of Saudi oil a day, or about 8 per cent of the world's total output.
The development comes after US Secretary of State Mike Pompeo said in a tweet that "Tehran is behind nearly 100 attacks on Saudi Arabia while (President Hassan) Rouhani and (Foreign Minister Mohammad Javad) Zarif pretend to engage in diplomacy".
He also dismissed claims by the Yemeni Houthis that they were responsible for the attacks saying "there is no evidence the attacks came from Yemen".
On Sunday, Iranian Foreign Ministry spokesman Abbas Mousavi called Pompeo's allegations "meaningless and incomprehensible in diplomatic standards".
Iran is yet to comment on Monday's development.
The attacks habe cut global oil supplies by 5 per cent and the prices have also soared, the BBC reported.
Brent crude jumped 10 per cent to $66.28 a barrel - the biggest one-day rise since the 1991 Gulf War.
Prices eased slightly after President Trump authorised the release of US reserves. But there were concerns that higher prices could continue if tensions worsen further.
( With inputs from IANS )