Flight records show two Saudi planes arrived at Istanbul's Ataturk airport on Tuesday and departed separately that same day, hours after Khashoggi was last seen.
"We call on the government of Saudi Arabia to support a thorough investigation of Mr Khashoggi's disappearance and to be transparent about the results of that investigation", Pompeo said in a statement.
The surveillance image released by the Post bore a date and time stamp, as well as a Turkish caption bearing Khashoggi's name and that he was arriving to the consulate. That team was sent "specifically for the murder", a person with knowledge of the Turkish investigation tells the Post.
His disappearance has sparked global concerns, particularly after Turkish sources said over the weekend that authorities believed he had been killed inside the consulate.
Mr Khashoggi, 59, went missing while on a visit to the consulate in Istanbul for paperwork to marry his Turkish fiancée. The French foreign ministry said Khashoggi was "a recognised and respected Saudi figure".
David Rohde, executive editor of The New Yorker tweeted out, "The journalist Jamal Khashoggi had said that the Saudi crown prince, Mohammed bin Salman, has 'no tolerance or willingness to accommodate critics'".
"Normally we'd also have an ambassador in Saudi Arabia".
That kind of big-time money is essential to the crown prince's ambitious plans to develop the kingdom, to diversify the economy beyond the oil.More news: Hurricane Michael is a rare, but not unprecedented, October storm
Over the past year, he has written columns for newspapers including the Washington Post criticising Saudi policies towards Qatar and Canada, the war in Yemen and a crackdown on dissent which has seen dozens of people detained. Relations were already strained after Turkey sent troops to the Gulf state of Qatar previous year in a show of support after its Gulf neighbours, including Saudi Arabia, imposed an embargo on Doha.
Turan Kislakci, a friend of Khashoggi and the head of the Turkish-Arab Media Association, spoke to the AP on Sunday outside the Saudi Consulate in Istanbul.
A Saudi official said Khashoggi left the consulate shortly after he visited. "God willing, we will not face an undesired situation", he told reporters, avoiding confirming claims that the journalist was killed.
Almost a week since Khashoggi disappeared, Recep Tayyip Erdogan stepped up his calls for Riyadh to explain what happened to the high-profile critic of the Saudi leadership.
"Do you not have cameras and everything of the sort?" She accused Saudi Arabia of "state terrorism" and called on the worldwide community to take action against the kingdom. Then why do you not prove this?
Turkey has summoned the Saudi ambassador to request the kingdom's "full cooperation" in an investigation into the disappearance of Khashoggi, a Washington Post contributor who wrote articles critical of the Kingdom's ruling elite.
Ties between Ankara and Riyadh are at a low point over Turkey's support for Qatar in its year-long dispute with Saudi Arabia and other Gulf nations. Also, Ankara has continued to encourage Saudi investments in Turkey, with the Saudis eyeing especially the real estate sector.
But Mr Dalay said Mr Khashoggi was not a political dissident.