The statement carried by the state-run Saudi Press Agency also warned that the kingdom would respond to any steps taken against it with “greater action.”
“The kingdom affirms its total rejection of any threats and attempts to undermine it, whether by threatening to impose economic sanctions, using political pressures, or repeating false accusations,” it read.
While the statement did not directly refer to Khashoggi or Trump, it came a day after the president vowed to “get to the bottom” of the journalist’s disappearance in an interview with CBS’ “60 Minutes.”
Asked whether Saudi Crown Prince Mohammed bin Salman gave an order to kill Khashoggi, Trump said "nobody knows yet, but we'll probably be able to find out."
"We would be very upset and angry if that were the case," Trump added.
Khashoggi is a Saudi citizen and critic of the government who vanished on Oct. 2 after entering the consulate, triggering a major diplomatic crisis for the kingdom.
The Saudi government has denied and condemned the allegations that it killed Khashoggi.
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Late Sunday, a slew of Arab countries and organizations came out in support of Saudi Arabia, condemning what they called false accusations and reports. These included Egypt, Yemen, Jordan, Oman, United Arab Emirates, the Palestinian Authority, Kuwait, the Cooperation Council for the Arab States of the Gulf and Arab League.
In the clip CBS released ahead of Sunday's broadcast, Trump said his son-in-law Jared Kushner had spoken with the crown prince, who repeatedly denied having anything to do with Khashoggi's disappearance.
"They deny it. They deny it every way you can imagine. In the not too distant future I think we'll know an answer," the president said.
Saudi Arabia's interior minister said in a statement Saturday that the allegations that the Saudi government committed the killing of Khashoggi "are outright lies and baseless allegations."
The statement went on to say that Saudi Arabia is "committed to its principles, rules and traditions and is in compliance with international laws and conventions."
However, despite the denial, mounting evidence that the Saudis were involved has fueled a growing outcry from foreign governments, U.S. lawmakers and the Trump administration, all of whom have demanded more information.
In a joint statement on Sunday, Germany, France and Britain called for a "credible investigation" into what happened to Khashoggi and "if relevant" identify those responsible for his disappearance.
“We encourage joint Saudi-Turkish efforts in that regard, and expect the Saudi government to provide a complete and detailed response,” they added.
Turkish authorities have told U.S. officials that they have recordings from inside the Saudi consulate in Istanbul that provide evidence that Khashoggi was killed inside, officials told NBC News.
The recordings were key to Turkey being confident enough to say that Khashoggi is dead and that Saudi Arabia killed him, according to both U.S. and Turkish officials, along with other individuals briefed on the intelligence. The Washington Post first reported on the recordings.
The existence of the recordings sheds light on how Turkey was able to conclude so quickly that Khashoggi never left the consulate, as Saudi Arabia has claimed. A senior Turkish official earlier told NBC News that Turkey has 100 percent confidence that Khashoggi was killed in the consulate by a 15-member Saudi team that stayed in Turkey for a brief period and then left.
The Saudi statement on Sunday said the Kingdom faced a campaign of “false allegations and falsehoods" but insisted they would not be undermined.
"The Kingdom as the government and people are steadfast, glorious as ever, no matter whatever the pressures and circumstances might be.”
It came after the Tadawul exchange in Riyadh dropped by 7 percent at one point during the week’s first day of trading, with 182 of its 186 listed stocks showing losses by the early afternoon. The market clawed back some of the losses, trading down over 4 percent later on.
The crown prince has aggressively pitched the kingdom as a destination for foreign investment. But Khashoggi’s disappearance, and suspicions he may have been targeted over his criticism of the crown prince, have led several business leaders and media outlets to back out of an upcoming high-profile investment conference in Riyadh.
Trump made a point of visiting the kingdom on his first overseas trip as president and has touted arms sales to Saudi Arabia. In his CBS interview the president reiterated earlier concerns that any punishment shouldn't affect trade with Saudi Arabia, signaling that cutting off U.S. military sales to the kingdom may not be an option.