ISTANBUL — The disappearance of the Saudi dissident Jamal Khashoggi is opening a rift between Washington and Saudi Arabia as the kingdom blasted President Trump on Sunday for promising “severe punishment” if the royal court was responsible.

If Saudi Arabia “receives any action, it will respond with greater action,” the Saudi Foreign Ministry said in a statement, citing the oil-rich kingdom’s “influential and vital role in the global economy.”

Saudi Arabia “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,” the Foreign Ministry said.

The “accusations” at issue are the claims of Turkish officials that a team of Saudi agents killed and dismembered Mr. Khashoggi, a United States resident and columnist for The Washington Post who was last seen entering the Saudi Consulate in Istanbul on the afternoon of Oct. 2.