The United States said on Monday the war with Iran could be over "very soon", but Tehran said on Tuesday it would keep fighting as long as necessary.

"We're ahead of our initial timeline by a lot," US President Donald Trump said at a news conference on Monday afternoon. He previously estimated the operation could take several more weeks.

He told lawmakers the war would continue until Iran is "totally and decisively defeated", but predicted it would be over soon, saying the campaign would be a "short-term excursion".

"We've already won in many ways, but we haven't won enough," he said.

However, he did not define exactly what victory in the war would look like.

In an interview, Iran's Foreign Minister Seyed Abbas Araghchi told the US' PBS News that "the firings continues, and we are prepared".

"We are well-prepared to continue attacking them with our missiles as long as needed and as long as it takes," he said.

Iran's Islamic Revolutionary Guard Corps also responded to Washington that they would "determine the end of the war".

Iranian state media showed large crowds in several cities rallying behind their new supreme leader, Mojtaba Khamenei, waving Iranian flags.

The US said more than 5,000 targets in Iran had been hit as of Monday, about 10 days after hostilities began.

In response to concerns that Iran could block the Strait of Hormuz, a vital artery for oil shipments, Trump said the passage "is going to remain safe", adding that the US navy would escort oil tankers if necessary.

French President Emmanuel Macron said on Monday that his country and its allies were working on a "purely defensive" mission to reopen the strait, aiming to escort ships "after the end of the hottest phase of the conflict".

On Friday, Trump said he would only accept "unconditional surrender" from Iran, which he claimed posed an imminent nuclear threat.

Kamal Kharazi, foreign policy adviser to the office of Iran's supreme leader, ruled out the possibility of talks at the moment and said the war would only end through economic pain.

"I don't see any room for diplomacy anymore. Because Donald Trump had been deceiving others and not keeping with his promises, and we experienced this in two times of negotiations — that while we were engaged in negotiation, they struck us," Kharazi told CNN on Monday.

"There's no room unless the economic pressure would be built up to the extent that other countries would intervene to guarantee termination of aggression of Americans and Israelis against Iran," he said, suggesting that Gulf Arab countries and others need to put pressure on the US to end the war.

Oil benchmark drops

Although crude oil futures spiked on Monday morning, with West Texas Intermediate nearing $120 a barrel, prices fell later in the afternoon, with Brent crude settling around $90 per barrel, and WTI dropping to around $94.

Factors such as the disruption of shipping in the Strait of Hormuz, spreading conflict in the region, as well as production cuts by major Middle Eastern oil producers have significantly affected these prices, oilprice.com reported.

According to a Reuters/Ipsos poll released on Monday, 67 percent of people in the US expect gasoline prices to rise this year. That represented 44 percent of Republicans and 85 percent of Democrats.

On Monday, the US administration said it may remove tariffs or sanctions on some countries to help moderate the price of oil.

In addition, 60 percent of respondents expect that US military involvement in Iran will "go on for an extended period of time", according to the poll.

Agencies contributed to this story.