ISTANBUL — President Recep Tayyip Erdogan of Turkey swept into Ankara’s wood-paneled Parliament on Tuesday to level his most direct attack yet against Crown Prince Mohammed bin Salman of Saudi Arabia, accusing his government of planning the “savage murder” and mutilation of the dissident writer Jamal Khashoggi.

Hours later, Prince Mohammed bounded into the gilded conference hall of the Ritz-Carlton Hotel in Riyadh to a standing ovation from scores of oil executives, bankers and other businessmen who had risked association with scandal over the killing of Mr. Khashoggi for a chance to profit from the kingdom’s vast wealth.

“More people, more money,” the crown prince told reporters, pronouncing the event a success despite the withdrawal of dozens of speakers and the pleas of many businessmen for him to spare them embarrassment by calling it off.

Their competing stage shows on Tuesday were the latest salvos in an increasingly high-stakes battle that no longer appears to leave either one room for retreat, pitting against each other two American allies who have each aspired to be the leader of their region.