US President Donald Trump has foreshadowed a major escalation in the Iran conflict, warning that the “big one is coming soon.”

“We’re knocking the crap out of them,” Trump told CNN on Monday (US time).

“I think it’s going very well. It’s very powerful. We’ve got the greatest military in the world and we’re using it.”

Trump said the US-Israel operation was going to ramp up further.

“We haven’t even started hitting them hard. The big wave hasn’t even happened. The big one is coming soon,” he said.

The US and Israel launched surprise attacks on Saturday (AEDT), ‌killing Supreme Leader Ayatollah Ali Khamenei, sinking Iranian warships and hitting more than 1000 targets so far.

The attack triggered Tehran’s retaliation, with Iranian strikes hitting countries across the Middle East, throwing global air transport into chaos, shutting down shipping through the Strait ‌of Hormuz and sending oil prices surging.

Israel also attacked Lebanon in response to strikes by Hezbollah and Tehran kept up its missile and drone attacks on Gulf states.

Kuwait mistakenly shot down three American F-15E fighter jets during an Iranian attack on Monday (local time).

All six crew members ejected and were safely recovered. Video, filmed at a location verified by Reuters, showed one of the planes spiralling out of the sky, an engine ‌on fire.

Trump said the operation could continue for some weeks and that it was unclear who was in charge in Iran.

“We’re already substantially ahead of ‌our time projections. But whatever the time is, ⁠it’s okay,” he said at a Medal of Honour ceremony at the White House.

“Right from the beginning, we projected four to five weeks, but we have capability to go far longer than ​that.”

The Pentagon also gave its first update and played down concerns of another unending Iraq-style war.

“To the media outlets and political left screaming ‘ENDLESS WARS’ — stop. This is not Iraq. This is not endless,” Defence Secretary Pete Hegseth, a former Fox News host and army veteran, said.

The US and Israeli attacks have triggered a massive Iranian ​retaliatory response. Many of the most dangerous drones and missiles have been intercepted by US military forces and US allies in the region.

Even with the US-Israeli strikes, the conservative clerical leaders in Iran have shown no sign of yielding power. Military experts say US and Israeli air power, with no armed force on the ground, may not be enough to drive them out.

Hegseth said there were no US troops on ​the ground. But he also declined to rule that possibility out.

“We are not going into the exercise of [saying] what we will or will not do,” Hegseth said. “President Trump ensures that our enemies understand we’ll ​go as far as we need to go ⁠to advance American interests.”

“But we’re not dumb about it. You don’t have to roll 200,000 people in there and stay 20 years.”

-with AAP