After the statement was released, a Turkish official told the Washington Post -- for which Khashoggi was a contributor -- that authorities are investigating a theory the body was destroyed in acid, either in the consulate or the Saudi consul's nearby residence.
The Islamist group has branches in countries around the Middle East, and, to the Saudis, being a member made Khashoggi a terrorist. The murder has drawn withering criticism of Riyadh from around the world.
US Secretary of State Mike Pompeo has said it may take "a handful more weeks" before Washington has enough evidence to impose sanctions on individuals responsible for the killing of Saudi journalist Jamal Khashoggi.
After the journalist disappeared, Saudi Arabia initially insisted Khashoggi had walked out of the consulate after visiting the building on October 2.
Saudi Crown Prince Mohammed bin Salman has met with a delegation of pro-Israeli advocates in Riyadh amid reports that Israeli Prime Minister Benjamin Netanyahu has asked the U.S. to keep supporting the young prince against worldwide criticism. The Saudi attorney general has since acknowledged that Khashoggi was killed in a premeditated murder.
Khashoggi, who lived in the United States and wrote columns for the Washington Post, went to the Saudi consulate in Istanbul on October 2 to collect some documents, but he never reappeared.
Israeli officials confirmed the Post's report to the Ynet news site, saying Netanyahu urged officials in Washington not to allow the close relationship with the Saudi crown prince to be undermined by the incident.
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Exactly one month after the disappearance and the subsequent murder of the Washington Post columnist inside the Saudi consulate in Istanbul, the United States has yet to issue the "severe punishment" that Donald Trump had promised if the regime's involvement in the journalist's death were confirmed.
"Jamal Khashoggi was not a member of the Muslim Brotherhood. To claim otherwise would be ridiculous", the statement said. "The president said we will demand accountability for those who were involved in the commission of this heinous crime".
But we have significant interests related to Saudi Arabia.
On Wednesday Turkey said he was strangled immediately after entering the consulate and his body dismembered "in accordance with plans made in advance".
Turkey has steered away from publicly blaming Saudi Arabia for the killing.
US State Department spokesman Robert Palladino on Thursday called for Khashoggi's remains to be located and returned to his family for burial as soon as possible.