LONDON — Saudi Arabia charged Monday that a missile fired at its capital from Yemen over the weekend was an “act of war” by Iran, in the sharpest escalation in nearly three decades of mounting hostility between the two regional rivals.

“We see this as an act of war,” the Saudi foreign minister, Adel Jubair, said in an interview on CNN. “Iran cannot lob missiles at Saudi cities and towns and expect us not to take steps.”

The accusation, which Iran denied, came a day after a wave of arrests in Saudi Arabia that appeared to complete the consolidation of power by the crown prince, Mohammed bin Salman, 32. Taken together, the two actions signaled a new aggressiveness by the prince both at home and abroad, as well as a new and more dangerous stage in the Saudi cold war with Iran for dominance in the region.

“Today confrontation is the name of the game,” said Joseph A. Kechichian, a scholar at the King Faisal Center for Research and Islamic Studies in Riyadh, Saudi Arabia, who is close to the royal family. “This young man, Prince Mohammed bin Salman, is not willing to roll over and play dead. If you challenge him, he is saying, he is going to respond.”