Erdogan's address coincided with the start of an investment conference in Saudi Arabia that was briefly attended by the Saudi crown prince.
The bill said that President Donald Trump could request exceptions to the arms sale ban if he also submitted a report on a U.S. investigation into anyone involved in "the murder of journalist and United States permanent resident Jamal Khashoggi".
He said a team of Saudi agents arrived in Turkey on October 1, the day before Khashoggi's death, and some visited the woods around Istanbul; that area has been searched for the journalist's body, which has yet to be found.
Saudi Arabia initially claimed Khashoggi left freely after visiting the consulate but, as global pressure mounted, the kingdom said he died inside the mission when an argument degenerated into a fistfight.
May added that she will continue to pile diplomatic pressure on Saudi leaders to complete a swift and transparent investigation, and would be speaking to Saudi King Salman later Wednesday.
In addition to revoking visas, Mr Pompeo said the USA was looking into the possibility of imposing sanctions on those believed to be involved in Khashoggi's killing.
The Saudi kingdom has provided conflicting accounts of what happened to Khashoggi, a United States resident and Washington Post contributor.
The Turkish president said that the names of suspects provided by Saudi Arabia matched those identified by Turkish authorities during their investigation.
Still, Pompeo stressed the strategic importance of the US-Saudi relationship.
A 15-person team made up of senior Saudi officials meticulously planned the operation before his "gruesome" murder, including the use of a body double to falsely suggest Khashoggi had left the building alive, Mr Erdogan said.
Jamal Khashoggi is one of the Arab world's most prominent journalists and commentators.
"Haspel, who departed for a secret trip to Turkey on Monday, heard the audio during her visit, according to people familiar with her meetings", said the US daily.
Asked to confirm whether this was true, Cavusoglu said he could not provide an exact answer but Turkey would "share documents and evidence in our hands with countries and institutions which wanted it".