Hatice Cengiz made the appeal in an essay for The Washington Post newspaper on Tuesday.
A prominent critic of Riyadh, Khashoggi was last seen a week ago entering Saudi Arabia‘s consulate in Istanbul to get documents for his forthcoming marriage.
Turkish sources said they believed Khashoggi was killed inside the diplomatic post, a claim Saudi Arabia has dismissed as “baseless”.
In her essay, Cengiz said Khashoggi first visited the consulate on September 28 “despite being somewhat concerned that he could be in danger”.
But he walked in “because he did not believe that something bad could happen on Turkish soil”.
“It would be a violation of international law to harm, arrest or detain people at a diplomatic mission, he said, and noted that no such thing had ever happened in Turkey’s history,” Cengiz wrote.
After a positive meeting with consular staff who “welcomed him warmly”, Khashoggi “was relaxed” before his second visit on October 2, she said.
Cengiz, who waited for him outside, said he never emerged.
“At this time, I implore President Trump and first lady Melania Trump to help shed light on Jamal’s disappearance,” Cengiz wrote.
“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.”
She added: “Although this incident could potentially fuel a political crisis between the two nations, let us not lose sight of the human aspect of what happened.”
Cengiz’s request came as Turkey said it was preparing to search the consulate as part of an investigation to Khashoggi’s disappearance.
A surveillance video image obtained by Turkish newspaper Hurriyet also surfaced on Tuesday showing Khashoggi walking into the consulate in Istanbul’s upscale 4th Levent neighbourhood.
Meanwhile, The New York Times reported top Saudi leaders deployed a 15-man hit squad to lay in wait for the dissident writer. Citing anonymous Turkish officials, the newspaper said the assassination team included a forensic expert who brought a bone saw to dismember Khashoggi’s body.
Turkish police have previously said a team of 15 Saudis were sent to Istanbul and were in the building at the same time as Khashoggi.
Turkish security officials were working to identify the 15 individuals, English-language state broadcaster TRT World reported, adding that Turkish officials believe the Saudis may have taken the consulate’s CCTV footage with them when they returned to Riyadh.
According to pro-government daily Sabah, the team arrived in Istanbul on two private planes, one which landed after 03:00 am (00:00 GMT) on Tuesday while the second plane landed around 05:00 pm (14:00 GMT) after Khashoggi entered the consulate.
The individuals checked into two hotels close to the consulate, the daily said.
Both planes later returned to Riyadh with one stopping in Dubai and the other in Egypt, Sabah reported, adding the police were looking into the possibility that Khashoggi was kidnapped.
Separately, The Washington Post – for whom Khashoggi wrote columns – reported US intelligence intercepted communications of Saudi officials planning to abduct the writer.
“Saudis wanted to lure Khashoggi back to Saudi Arabia and lay hands on him there,” the Post quoted a person familiar with the information as saying.
It was not clear whether the Saudis intended to arrest and interrogate Khashoggi or to kill him – or if the US warned Khashoggi he was a target, the source told the newspaper.
Khashoggi, who wrote critically for the Post about Crown Prince Mohammed bin Salman‘s rise to power, had been in a self-imposed exile in the US since last year, fearful of the prince’s low tolerance for criticism.
Cengiz wrote that he also sought to become a US citizen.
“Although my hope slowly fades away each passing day, I remain confident that Jamal is still alive,” she wrote.
“Perhaps I’m simply trying to hide from the thought that I have lost a great man whose love I had earned.”