Oil tankers are crossing the Strait of Hormuz and Iran's actions to choke traffic through the shipping route have not hurt the U.S. economy, White House economic adviser Kevin Hassett told CNBC on Tuesday, reiterating the Trump administration's position that the war should be over in weeks, not months.

"Already you're seeing tankers are starting to dribble through the straits, and I think it's a sign of how little Iran has left," he said.

"We're very optimistic that this is going to be over in the short run, and then there will be price repercussions when it is over for a few weeks, as the ships make it to the refineries."

Hassett said there is concern that Asia may not be exporting as much refined oil to the U.S. to handle a decrease in supply from the Middle East.

"We're seeing some signs that they might be pulling that back to make sure that they have enough energy for themselves. And we've got a plan for that," he said.

Trump on Monday postponed his meeting with Chinese President Xi Jinping to focus on the war in Iran. Hassett said the US action in Iran is in China's interest.

"This is one case where the objectives of both countries are aligned, that we want, you know, a stable world oil market," he said. "When this war is over, which will be sometime soon, I'm sure they'll get together and have a lot to talk about, and hopefully, when the Chinese express some gratitude."