Those behind the killing in the Saudi consulate in Istanbul three weeks ago “should be in big trouble”, he said.
Shortly afterwards, Secretary of State Mike Pompeo said the US would “punish those responsible” and had revoked visas of 21 identified suspects.
The Saudi government has blamed the murder on rogue agents.
But President Erdogan of Turkey has said the journalist was the victim of a carefully planned “political murder” by Saudi intelligence officers and other officials.
Speaking to reporters at the White House on Tuesday, Mr Trump said: “They had a very bad original concept, it was carried out poorly and the cover-up was the worst in the history of cover-ups.
“Whoever thought of that idea, I think is in big trouble. And they should be in big trouble.”
The Saudi government has provided conflicting accounts of what happened to Khashoggi, a US resident and Washington Post contributor. After weeks of maintaining he was still alive, senior officials now say the 59-year-old was murdered in a rogue operation after visiting the Saudi consulate in Turkey.
European Council President Donald Tusk said EU member states must pursue the full details of the killing and avoid any “trace of hypocrisy”.
In a speech to the European Parliament, Mr Tusk said he expected member states and institutions to avoid any “ambiguous game”.
What has Trump said?
Mr Trump’s public criticism of Saudi Arabia on Tuesday was his strongest so far, but he has continued to highlight the kingdom’s importance as a US ally.
In a separate interview with the Wall Street Journal, Mr Trump addressed the possible involvement of Saudi royals in the killing and said he did not believe King Salman had prior knowledge of the operation.
When asked about the possible role of Crown Prince Mohammed bin Salman, the president replied: “He’s running things and so if anybody were going to be [informed], it would be him.”
He said he had questioned the crown prince about Khashoggi’s death, and been told he did not know about the operation when it was being planned.
Asked if he believed the royal family’s denial, Mr Trump reportedly gave a long pause before saying: “I really want to believe them.”