"You never like to say too early you won. We won," Trump told a campaign-style rally in Kentucky. "In the first hour it was over."
He said the US had knocked out 58 Iranian naval ships.
Trump has seesawed on Iran, crediting the US military for significantly degrading Iran's military but resisting a speedy end to the conflict.
"We don't want to leave early do we?" Trump said. "We got to finish the job."
He said the United States has "virtually destroyed Iran" but seemed to signal the US would continue the fight for now.
"We don't want to go back every two years," he said.
Trump had earlier told news outlet Axios in a phone interview the war with Iran will end soon because there is "practically nothing left to target".
"Any time I want it to end, it will end," Trump said.
Earlier, Iran's military said the world should be prepared for oil to hit $US200 a barrel as its forces attacked merchant ships in the blockaded Gulf.
The International Energy Agency, made up of major oil consuming countries, recommended releasing 400 million barrels from global strategic reserves to stabilise prices, the biggest such intervention in history, which was swiftly endorsed by the United States.
But the rate at which countries can release it would account for just a fraction of the supply through the Hormuz Strait, where a fifth of the world's oil has been blockaded behind a narrow channel along the Iranian coast.
"Get ready for oil to be $US200 a barrel because the oil price depends on regional security, which you have destabilised," Ebrahim Zolfaqari, spokesman for Iran's military command, said in comments addressed to the US.
Oil prices, which shot up briefly to nearly $US120 a barrel on Monday, have since settled around $US90, suggesting investors are betting on a swift end to the war and reopening of the strait.
Iranian officials made clear on Wednesday they intended to impose a prolonged economic shock as the war carries on.
After offices of a bank in Tehran were hit overnight, Zolfaqari also said Iran would respond with attacks on banks that do business with the United States or Israel.
Iran's Revolutionary Guards said their forces had fired on two ships in the Gulf that had disobeyed their orders.
One, a Thai-flagged bulk carrier, was set ablaze, forcing the crew to leave, with three people reported missing and believed trapped in the engine room.
Reuters could not verify the second incident described by the Guards involving what they described as a Liberian-flagged ship.
But two other ships, a Japanese-flagged container ship and a Marshall Islands-flagged bulk carrier, were reported to have sustained damage from projectiles.
The strikes raised the number of merchant ships that have been hit since the war began to 14.
A senior Israeli official told Reuters Israeli leaders now privately accepted that Iran's ruling system could survive the war.
Two other Israeli officials said there was no sign the US was close to ending the campaign.
In the latest public display of defiance, huge crowds of Iranians took to the streets on Wednesday for funerals for top commanders killed in air strikes.
An Iranian official told Reuters that Mojtaba Khamenei had been lightly wounded early in the war, when air strikes killed his father, mother, wife and a son.
He has not appeared in public or issued any direct message since the war began.
The Iranian military said on Tuesday it had launched missiles at targets including a US base in northern Iraq, the US naval headquarters for the Middle East in Bahrain and at targets in central Israel.
Explosions rang out in Bahrain while in Dubai four people were wounded by two drones that crashed near the airport.
At Oman's Port of Salalah, firefighters battled a blaze at fuel storage tanks after days of Iranian attacks, according to the Oman News Agency.
With AP
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