Turkish officials say they believe Khashoggi, a critic of Salman who has been living in self-imposed exile in the US, was murdered October 2 inside the consulate when he went there to pick up documents to allow him to marry Cengiz, a Turkish national, or perhaps spirited away to Riyadh. "We don't have any information on that", State Department spokeswoman Heather Nauert told reporters Tuesday.
The kingdom calls the allegation "baseless", but has not offered any evidence to explain why Mr Khashoggi simply walked out of the consulate and disappeared though his fiancée waited outside for him.
In a letter to President Donald Trump Wednesday, senators invoked the Global Magnitsky Act of 2016 to seek an investigation into what happened to Khashoggi, a Washington Post Global Opinion columnist.
Both Turkey and Saudi Arabia are allies of the United States. "We're probably getting closer than you might think but I have to find out what happened".
This image taken from surveillance camera shows a still image of people inside Ataturk International Airport, Istanbul, Turkey, on October 2, 2018.
"Nobody knows what happened", he said.
"And we have investigators over there and we're working with Turkey, and frankly we're working with Saudi Arabia". We're looking at it very strongly.
"I also urge Saudi Arabia, especially King Salman and Crown Prince Mohammed bin Salman, to show the same level of sensitivity and release CCTV footage from the consulate", Cengiz wrote.
More than 20 Republican and Democratic senators instructed Trump to order an investigation under legislation that authorizes imposition of sanctions for perpetrators of extrajudicial killings, torture or other gross human rights violations.
He continued: "Part of that is what we're doing with our defense systems and everybody's wanting them".
Meanwhile, Mr Trump told reporters in the Oval Office that he has a call in to Mr Khashoggi's fiancee, Hatice Cengiz, who has appealed to the president and first lady Melania Trump for help.
Mr Trump's remarks, on the other hand, came as prominent American lawmakers increasingly criticise Saudi Arabia - America's longtime security ally in the region.
'There's a sense of entitlement, I hate to use the word, arrogance, that comes with dealing with them, ' said Sen.
Erdogan, whose AK Party is rooted in political Islam, also supported a government in Egypt led by the Muslim Brotherhood, which Saudi Arabia has designated a terrorist movement.
He said all of the facts must be corroborated, but he fears the situation is going to "take a negative turn pretty quickly" if the most recent reports are accurate.
Khashoggi went missing from the Saudi Consulate in Istanbul on October 2, 2018.
But Trump, who during his first official visit to Saudi Arabia in May 2017 announced a proposed $110 billion arms deal with the kingdom, wouldn't say whether he would block further weapons sales if it is proven that the crown prince was behind Khashoggi's disappearance.
The Khashoggi incident might make it very hard for the Trump administration to win congressional approval for arms sales to the Saudis.
He added, "The Saudis continue to claim that they aren't targeting civilians inside Yemen, but how can we believe them when they apparently just hunted down and murdered an American resident whose only offense was writing critical articles about the Saudi royal family?"
This is while Riyadh had denied being behind Khashoggi's disappearance.
In Washington, State Department spokeswoman Heather Nauert said that the Saudi ambassador to the US was traveling to Saudi Arabia, and that the USA expects him to provide information about the Khashoggi case when he returns.