"I said, 'nope, you are not making 18-hour flight to go there. We have all the cards,'' Trump was quoted as saying by Fox News.
At the same time, the US remains open to negotiations with Iran, Trump said.
"You are not going to be making any more 18-hour flights to sit around talking about nothing," the president added.
Trump said that the cancellation of the trip by Witkoff and Kushner did not mean a resumption of US attacks, Axios reported.
The US president also said that there is "infighting and confusion" within Iran's leadership, while the trip would have required significant time and effort.
"‘Nobody knows who is in charge, including them. Also, we have all the cards, they have none! If they want to talk, all they have to do is call!!!" Trump said on Truth Social.
On February 28, the United States and Israel launched strikes on targets in Iran, including in Tehran, causing damage and civilian casualties. On April 7, Washington and Tehran announced a two-week ceasefire. Subsequent talks in Islamabad ended without result. While no resumption of hostilities was announced, the US began a blockade of Iranian ports. Mediators are attempting to organize a new round of talks.
Iranian Foreign Minister Abbas Araghchi arrived in Pakistan, which is mediating between Tehran and Washington, on Friday. Witkoff and Kushner were expected to travel there on Saturday. The Iranian delegation, according to some reports, has already left Pakistan.