Washington (CNN) President Donald Trump said he is not giving cover to Saudi Arabia over the suspected killing of journalist Jamal Khashoggi, as his top diplomat said Riyadh needed space and time to conduct an investigation.

But as details continue to emerge about Khashoggi's suspected murder inside the Saudi consulate in Istanbul on Oct. 2 -- and sources float the possibility that blame will fall on a "rogue" operative -- the administration's effort to defend Saudi Arabia is creating pushback and raising questions about Trump's potential conflicts of interest.

Some lawmakers are calling for an independent international inquiry as others are asking the President to report to Congress within a month about any personal financial ties he might have to the Kingdom that might create conflicts of interest.

"According to public reports, the Trump Organization for decades has maintained business relationships with the government of Saudi Arabia and members of the Saudi royal family," a group of Democratic senators wrote the President on Wednesday.

"Your recent statements, and public reports of increased spending by the Saudi government at Trump properties, raise significant concerns about financial conflicts of interest," the lawmakers wrote

'Not a small matter'

While Trump insisted this week he has no financial interests in Saudi Arabia, he has boasted publicly about money he's made from Saudi property investors and Saudis have poured money into Trump Hotels since the President's election.

A lobbying firm for Saudi Arabia paid more than $270,000 to the Trump International Hotel in Washington between October 2016 and March 2017, and The Washington Post has reported that Trump Hotels in New York and Chicago have benefited from a rush of visitors from Saudi Arabia in recent months.

Nebraska Sen. Ben Sasse became the latest Republican to raise concerns about Trump's handling of the Saudi matter, telling CNN's Christiane Amanpour that "I think we're going to need an international investigation" into Khashoggi's alleged death.

"This is not a small matter that will be swept under the rug," Sasse said, adding that he hoped Trump was listening to information from his intelligence services, "not just the arguments that are coming from Saudi officials."

He was echoed by California Democratic Sen. Dianne Feinstein, who sits on the intelligence committee. "Instead of accepting King Salman and the crown prince's denials without any evidence or outlandish theories that he was killed by rogue agents, President Trump should immediately push for an international investigation into Khashoggi's disappearance," Feinstein wrote Wednesday in a Mercury News op-ed.

In separate remarks Wednesday, both Trump and Secretary of State Mike Pompeo continued their effort to create time for leaders in Riyadh to provide an explanation for Khashoggi's disappearance.

"I'm not giving cover at all," Trump said, when asked if he was providing cover for Saudi Arabia. "I just want to find out what's happening." The President has said that Saudi Crown Prince Mohammed bin Salman, the kingdom's defacto ruler, has strongly denied involvement in Khashoggi's suspected murder.

But several officials CNN has spoken with say the suspected killing could not have happened without the direct knowledge of the 33-year-old crown prince, who is known by his initials "MBS."

'A big factor'

Sources have told CNN the Saudis are preparing to say that Khashoggi died during an interrogation at the consulate, and three sources familiar with the case told CNN that responsibility lies with a high-ranking intelligence officer who has ties to the crown prince.

The emerging narrative seems designed to insulate the Saudi leadership from responsibility.

Even as signs point to close ties between the crown prince and some of 15 Saudis suspected of involvement in Khashoggi's disappearance, the President made it clear in a Wednesday interview with Fox Business that the administration would find it acceptable if King Salman and the crown prince were found to be unaware of the killing.

"That's a big factor in my eyes," Trump said.

Trump and Pompeo also stressed the various foreign policy reasons for defending Saudi Arabia on Wednesday.

"Saudi Arabia has been a very important ally of ours in the Middle East," Trump said, pointing to a US-Saudi arms deal that he valued at $110 billion, even though just $14.5 billion of that figure has actually begun to materialize.

Pompeo, speaking to reporters in Brussels after stops in Saudi Arabia and Turkey, said "we need to make sure we are mindful" of the important US-Saudi ties as the administration makes its conclusion about what happened to Khashoggi and evaluates the results of a Saudi investigation into the affair.

"I do think it's important that everyone keep in their mind that we have lots of important relationships -- financial relationships between US and Saudi companies, governmental relationships, things we work on together all across the world, the efforts to" counter Iran, Pompeo said to reporters in Brussels.

"Those are important elements of US national policy that are in American's best interest and we just need to make sure that we are mindful of that as we approach decisions that the United States government will take when we learn all of the facts associated with whatever may have taken place," Pompeo said.

Asked why the US seemed to give Saudi Arabia the benefit of the doubt, given the preponderance of signs that there was high-level Saudi involvement, Pompeo said "it is reasonable to give them a handful of days more to complete it, so they get it right, so that it's thorough and complete."

Possible audio evidence

But it was unclear how much information Pompeo himself had gleaned, or had been interested in gathering. When asked Wednesday whether Saudi officials had told him whether Khashoggi was dead or alive, he responded: "I don't want to talk about any of the facts, and they didn't want to either."

Pompeo and Trump spoke as Turkish media published grisly details they said was from an audio recording of Khashoggi's killing within the Saudi consulate, which reportedly suggests that the father of four was tortured and then killed soon after he entered the consulate.

Turkish officials have told CNN that Khashoggi's body was dismembered after he was killed in the consulate, and a source said that the father of four, who was 59 years old when he disappeared, may have been injected with some kind of tranquilizer.

Trump told reporters Wednesday that the US has asked Turkey for a copy of the audio it claims to have, but the President suggested he has doubts about whether the recording actually exists.

"We have asked for it, if it exists," the President said. "I'm not sure yet that it exists. Probably does. Possibly does."

Trump said he expected to "have a full report on that from Mike [Pompeo] when he comes back." The two are scheduled to meet on Thursday morning to discuss the matter.