"State Department senior officials have spoken with the Kingdom of Saudi Arabia through diplomatic channels about this matter".
Trump, whose first overseas trip as US president was to the kingdom and whose son-in-law Jared Kushner has close ties to Prince Mohammed, said Tuesday he had not yet talked to the Saudis about Khashoggi, "but I will be at some point".
The country's Crown Prince Mohammed bin Salman previously said Turkish authorities were welcome to conduct a search and his country had nothing to hide. They also stated that they saw diplomatic vehicles entering and leaving the premises. However, the consulate has other entrances and exits as well, through which Saudi officials insist he left.
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'".
Saudi Arabia has called accusations it ordered the killing of journalist Jamal Khashoggi inside its Istanbul consulate "lies and baseless allegations".
Mogherini added: "We expect a thorough investigation and full transparency from the Saudi authorities on what has happened".
The Kentucky Republican, who's close to President Donald Trump, has always been a critic of the Saudi government.
The head of the Turkish-Arab Media Association, Turan Kislakci, told the New York Times that Turkish police officers providing security for the consulate had checked their security cameras and did not see the journalist leave on foot.
United Nations human rights experts have called for an immediate worldwide investigation into the disappearance of a Saudi journalist who went missing after visiting the Saudi Consulate in Istanbul, with one insisting the case "should not be politicized".
The Saudi consul-general allowed reporters to tour the facility on Saturday to satisfy themselves that Khashoggi was not held within.
Turkey said Tuesday it would search the Saudi Consulate.
The 59-year-old Khashoggi went missing while on a visit to the consulate in Istanbul for paperwork to marry his Turkish fiancée.
Mr Hunt's intervention followed the publication of a CCTV image apparently showing Mr Khashoggi walking into the Saudi consulate in Istanbul, just before he went missing.
Ankara and Riyadh have given contradictory versions of the circumstances of Khashoggi's disappearance, with Turkish officials saying they believed he was still inside the consultate. The newspaper said the USA should demand answers from the Saudis.
U.S. Sen. Chris Murphy, the Connecticut Democrat who sits on the Senate's Committee on Foreign Affairs, expressed shock over the news.
Earlier on Wednesday, Turkish media outlets published CCTV footage which they say shows evidence of a plot linked to Mr Khashoggi's disappearance. "Now, nobody will dare to speak and criticize the reforms", Khashoggi said.
Khashoggi covered al Qaeda as a foreign correspondent in Afghanistan and Sudan and was well known for his several interviews with Osama bin Laden.
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.