Until Friday, the Saudi kingdom denied knowledge of his whereabouts and insisted he had left the building alive.
"If the President will not stand up to Saudi Arabia, then we in Congress must stand strong for our nation, our values and journalists throughout the world", Costa said.
Turkish officials say they also have an audio tape that purports to record Khashoggi's killing, but the tape has not been shared with American or Saudi officials.
The public prosecutor said a total of 18 people, all Saudi nationals, have been detained in connection to the probe.
He added that Saudi Arabia will not hesitate to form a joint investigation committee with Turkey to uncover the truth.
The Saudi prosecutor said on Friday that an investigation showed that Khashoggi's death was a result of a physical altercation at the Saudi consulate in Istanbul two weeks ago.
Investigators are examining traffic records of every vehicle that went in and out of the Saudi consulate.
The official, Leyla Sahin Usta, said it would have been "more valuable" if Saudi officials had earlier admitted that Khashoggi was killed in its diplomatic post.
Saudi Arabia also noted that the suspect tried "to hide what happened and to cover it up".
The announcement marks the first time that Saudi officials have acknowledged that Jamal Kashoggi was killed inside the consulate in Turkey.
Saudi has not yet named any of their suspects.
Al-Qahtani, a law graduate, served as media adviser to Mohammed bin Salman after holding several positions within the royal court. Gen. Ahmed al-Assiri.
The user posted (rough translation): 'I extend my honest thanks and gratitude to His Holiness the Custodian of the Two Holy Mosques and His Highness the Crown Prince, for the great confidence they have placed in me and for this great opportunity to honor my national service over the past years.
"I will remain a loyal servant to my country for all times", he wrote in a Twitter post on Saturday. Bin Salman says his kingdom's authorities are in talks with the Turkish government to determine what happen.
Trump has sent mixed messages about Khashoggi for days, vowing a severe response but also saying that the United States wants to preserve its close relationship with the conservative kingdom.
His disappearance has been shrouded in mystery and tipped Saudi Arabia into one of its worst global crises.
It effectively dismissed Turkish claims that he had been murdered by a Saudi hit squad flown into the country for the job, and insulated Mohammed Bin Salman, the young Saudi crown prince, from blame.
It called on Saudi authorities to produce Khashoggi's body so independent forensic experts could perform an autopsy. "He will have been aware of the general instruction to tell people to come back", the official said.