The US president said America plans to remain a “steadfast partner” of the kingdom.
Mr Khashoggi, a journalist and staunch critic of the Saudi rulers, was murdered inside the Saudi consulate in Istanbul on 2 October after entering to obtain documents so he could marry his Turkish fiancee.
Mr Trump said: “Our intelligence agencies continue to assess all information, but it could very well be that the crown prince had knowledge of this tragic event – maybe he did and maybe he didn’t!
“We may never know all of the facts surrounding the murder of Mr Jamal Khashoggi. In any case, our relationship is with the Kingdom of Saudi Arabia.
“The United States intends to remain a steadfast partner of Saudi Arabia.”
In a statement released by the White House, the president indicated he had no intention of cancelling $110bn in military contracts with Riyadh, saying: “If we foolishly cancel these contracts, Russia and China would be the enormous beneficiaries.”
Mr Trump also warned that oil prices would “skyrocket” if the US made a “terrible mistake” to break up with Saudi.
Saudi prosecutors are seeking the death penalty for five suspects charged with the journalist’s murder.
But the CIA is reported to have concluded that Saudi’s Crown Prince Mohammed bin Salman ordered his assassination – which he denies – and the 15 assassins flew on government planes to Turkey.
The US president said he has seen the report and claimed it is not “definitive”.
John Brennan, a former CIA director and fierce critic of Mr Trump, tweeted that the president “excels in dishonesty” so Congress will have to obtain the CIA findings of the “heinous act” which nobody should get away with.
Senator Jeanne Shaheen said the White House manoeuvre demonstrated “President Trump’s habit of siding with murderous foreign dictators over American intelligence professionals” and called this “a stain on our democracy”.
However, Mike Pompeo, the secretary of state, backed his boss, highlighting that the US relationship with the Saudis is bigger than the murder.
“It’s a mean, nasty world out there, the Middle East in particular,” he said.
“It is the president’s obligation, indeed the State Department’s duty as well, to ensure that we adopt policies that further America’s national security.
“So as the president said today, the United States will continue to have a relationship with the Kingdom of Saudi Arabia. They’re an important partner of ours.”
On Sunday Mr Trump said he had been fully briefed on a “vicious and terrible” audio recording of the killing but he could not bring himself to listen to it.
“I don’t want to hear the tape, [there is] no reason for me to hear the tape,” he said.
“It’s a suffering tape. It’s a terrible tape. It was very violent, very vicious and terrible.”
Turkey maintains it is in possession of a recording of the death, which it said had been shared with officials from Saudi Arabia, Germany, France, the US and the UK.
On Tuesday, Turkey’s foreign minister said the country could formally seek a UN investigation over the killing if co-operation with Saudi Arabia comes to an impasse.
But while Mr Trump and US vice president Mike Pence have both insisted they are determined to hold accountable those responsible for the murder, the White House has been reluctant to jeopardise its relationship with Riyadh.
Speaking to reporters before boarding Air Force One for a visit to fire-ravaged California over the weekend, Mr Trump said Saudi Arabia remained a “truly spectacular ally in terms of jobs and economic development”.
He denied the US had reached a conclusion on who was responsible for the murder of Mr Khashoggi.