Defense Secretary Lloyd J. Austin III stopped short on Thursday of blaming Iran for attacks that killed three U.S. service members on Sunday in Jordan but said that Tehran trained and funded the militia groups that have targeted American troops and commercial shipping in the Middle East.

Mr. Austin, in a rare show of bravado, continued the Biden administration’s promises of retribution. Asked why the administration was forecasting a dayslong campaign of retaliation, Mr. Austin said the Iran-backed militias “have a lot of capability.”

He paused and added, “I have a lot more.”

President Biden has promised that the United States will respond to Sunday’s attacks at a remote base used by American troops in Jordan. Those killed were Sgt. William Jerome Rivers, 46, of Carrollton, Ga.; Specialist Kennedy Ladon Sanders, 24, of Waycross, Ga.; and Specialist Breonna Alexsondria Moffett, 23, of Savannah, Ga. The Pentagon says that 40 American troops were injured.

Biden administration officials say that the drone strike crossed a red line and that there is no way the president will not respond.

Mr. Austin, during a news conference on Thursday, reiterated that. “We will respond when we choose, where we choose and how we choose,” he said.

Iran has signaled that it will not escalate tensions with the United States. The head of Iran’s Revolutionary Guards said on Wednesday that Tehran was “not looking for war.” And Kataib Hezbollah, the Iran-backed militia that American officials believe is responsible for the attack in Jordan, has said it would suspend military operations in Iraq, where it operates.

A statement by the group indicated that it had come under pressure from Iran and Iraq to stop attacking U.S. troops.

But the head of the Revolutionary Guards also warned that Iran was prepared to respond if attacked.

“You have tested us and we know each other — we will not leave any threat unanswered,” Gen. Hossein Salami, the chief commander of the powerful military organization, was quoted as saying by Iranian state news media.

Mr. Austin’s remarks came as the United States and another Iran-backed group, the Houthis of Yemen, engaged in a flurry of back-and-forth strikes on Thursday.

At about 1:45 a.m. local time, FA-18 Super Hornet attack planes from the aircraft carrier Dwight D. Eisenhower bombed a Houthi ground-control station and 10 unmanned attack drones in western Yemen that had been preparing to launch, the military’s Central Command said in a statement.

About three hours later, U.S. forces shot down an armed Houthi drone flying over the Gulf of Aden, Central Command said. About five hours after that, the military destroyed an explosives-laden naval drone that Central Command said was launched toward commercial ships and Navy vessels in the Red Sea. There were no injuries or damage reported in either incident.

Finally, around 12:45 p.m., two anti-ship ballistic missiles were launched from Houthi-controlled territory, probably toward a Liberian-flagged, Bermuda-owned cargo ship, M/V Koi, in the Red Sea, Central Command said. The missiles landed harmlessly in the water.

The United States has launched about 15 strikes against targets in Yemen since Jan. 11 in response to Houthi attacks on vessels in the Red Sea and the Gulf of Aden, most of them intended to destroy missiles and launchers capable of damaging ships.

The Houthis, an armed Shiite group that controls the west of Yemen, say they are attacking ships in solidarity with Palestinians who have been killed in an Israeli offensive against another Iran-backed militia, Hamas, which controls the Gaza Strip. The Houthis and Hamas share the goal of destroying Israel.