The disappearance of the Saudi dissident Jamal Khashoggi has set off a diplomatic feud between Saudi Arabia and Turkey, a bipartisan uproar in the United States Congress, tremors of uncertainty in Wall Street and Silicon Valley about how to deal with Saudi Arabia, and a noisy spat between the White House and its closest Arab ally.

On Monday morning, President Trump said on Twitter that he had just discussed the case with King Salman, who denied any knowledge of what had happened to Mr. Khashoggi, and that he was “immediately sending” Secretary of State Mike Pompeo to meet with the king. Later, in brief remarks to reporters, he said that from his conversation with the king, “it sounded to me like maybe these could have been rogue killers — who knows.”

[UPDATE: Jamal Khashoggi is dead. Here is everything we know so far.]

American officials have speculated that if Saudi Arabia confirms suspicions that Mr. Khashoggi was killed, it would propose that rogue elements acted on their own, not under orders from the highest levels of power in the kingdom. Turkish officials have described a grisly assassination and cover-up, with Saudi agents dismembering the body for disposal.

Turkish news organizations reported on Monday that Saudi Arabia would open its consulate to a search by investigators from both countries — something the kingdom has promised before but not yet allowed. And King Salman of Saudi Arabia reportedly ordered Saudi prosecutors to open their own investigation.