U.S. President Donald Trump has threatened "severe punishment" if it turns out Khashoggi was killed in the consulate, although he said Washington would be "punishing" itself if it halted military sales to Riyadh.
"When you sell arms to Saudi Arabia, it gives you leverage over them, because they need replacement parts, they need the training", Rubio said.
US senators called for reactions ranging from boycotting an upcoming economic summit in Riyadh to ending support for Saudi military operations in Yemen.
Turkish and Saudi authorities have now been told to launch a "credible investigation" into Mr Khashoggi's disappearance.
Doubts are also growing over whether British Trade Secretary Liam Fox will attend the Riyadh conference, the BBC reported Sunday citing diplomatic sources.
"What has reportedly happened in Turkey ... if proved true, would clearly change the ability of any of us in the West to do business with the Saudi government", he said in a statement.
Khashoggi went missing after visiting the Saudi Arabian consulate in Istanbul back on October 2.
Turki Aldakhil - US Sanctions on Riyadh Would Mean Washington Is Stabbing Itself
Trump said he plans to review recordings from the Turkish Government that purport to show evidence of Khashoggi's killing. I tell you want I don't want to do - Boeing, Lockeed, Raytheon, all those - I don't wanna hurt jobs.
King Salman also ordered Saudi prosecutors to begin an investigation into what happened to Mr Khashoggi, according to Reuters.
The Swiss government could decide on a case-by-case basis whether to impose economic sanctions on Saudi Arabia, a SECO spokeswoman was quoted as saying. Earlier in the week, President Trump appeared hesitant about the possibility of ending arms sales, even if Saudi Arabia is found to be culpable in the journalist's disappearance. Saudi officials call the allegations "baseless", but have offered no evidence Khashoggi ever left the consulate.
Hours before the announcement, Tadawul exchange in Riyadh dropped by as much as 7 percent during the week's first day of trading, with 182 of its 186 listed stocks showing losses by the early afternoon. "We believe it is not warranted given the long term relationship between the two countries, and Saudi being the swing oil producer".
There have been doubts, however, about how far the United States president is willing to go, given his administration's deep ties to Riyadh.
The admonitions of the United States emanating from Saudi Arabia "bring into question the essential pillars that underpin U.S. -Saudi relations", said Kristin Diwan, a scholar at the Arab Gulf States Institute in Washington.
Oil futures rose on Monday on concerns about supply, while stocks in Saudi Arabia fell sharply on Sunday.
Uber Technologies Inc Chief Executive Dara Khosrowshahi, Viacom Inc CEO Bob Bakish and billionaire Steve Case, one of the founders of AOL, said they were no longer going. "Saudi Arabia has a strategic value to the US that comes from its reliability in managing oil markets and coordinating intelligence".
Khashoggi, who was considered close to the Saudi royal family, had become a critic of the current government and Prince Mohammed, the 33-year-old heir apparent who has shown little tolerance for criticism.