Although Turkey has so far stopped short of officially blaming Saudi Arabia for the killing, investigators have said they have audio and video evidence which shows Mr Khashoggi, was killed by a team of Saudi agents inside the consulate.
"Their stories are all over the place", added Mr Trump.
Some governments and prominent executives have said they would pull out of a forthcoming investment conference in Saudi Arabia.
Earlier this week German Foreign Minister Heiko Maas said that there was "no basis" to continue arms sales to Saudi Arabia "as long as we don't know what happened".
"All of this needs to be explained in all its details", President Erdogan said on Sunday.
But a series of U.S. lawmakers of both parties expressed doubt, demanding a stronger stance against the longtime U.S. regional partner.
"Corker is also calling on Turkey, which has said it has tapes from Khashoggi's killing inside the Saudi Consulate in Istanbul, to turn them over to the United States".
After Saudi Arabia confirmed his death, she wrote on Twitter in Arabic: "They have taken your body from this world, but your lovely smile will stay in my world forever". Nobody has told me he's not responsible.
"We seek justice and this will be revealed in all its naked truth, not through some ordinary steps but in all its naked truth", Erdogan said on Sunday, according to the semiofficial Anadolu news agency.
"It could be something in the building went badly awry". Amid Trump's apparent equivocations, several key Republicans demanded a tougher stance. "He's seen as a person who can keep things under check", added Trump. "I don't think we need the Saudis".
"I would like to punish those involved".
For Saudi Arabia's allies - particularly in the West - the question will be whether they believe that the prince, who has painted himself as a reformer, has any culpability.
"This behaviour is outside the norm to the point that the people involved need to be removed in my view".
Pro-government media in Turkey have reported a different narrative, saying a Saudi hit squad of 15 people traveled to Turkey to kill the columnist for the Washington Post before leaving the country hours later in private jets. "I'm willing to separate the two", Mr Graham continued, accusing the prince of acting in a "barbaric fashion".
"The individuals who did this did this outside the scope of their authority", he added. Barring an unlikely "confession" from Prince Mohammed, Democratic congressman Adam Schiff said on Sunday that "the president is going to accept the crown prince's denials like he's accepted Putin's denials and Kim Jong-Un's denials".
"We're trying to ascertain the facts as to what happened in the consulate", he said.
King Salman expressed his deepest sympathy in a telephone call Sunday to Salah Jamal Khashoggi, the son of the 59-year-old journalist, who died in Istanbul early this month.