"I'm hearing little stories about Iran," Trump added. "If they do anything they will suffer greatly".
Saudi Arabia claimed that two of its oil tankers were attacked on Sunday while sailing toward the Persian Gulf.
The United Arab Emirates foreign ministry on Sunday reported that four commercial ships were attacked by an unknown adversary.
The precise nature of the incident remained unclear. Saudi Arabia's state run Saudi Press Agency described it as "a sabotage attack".
Iran's Foreign Ministry Spokesman Abbas Mousavi described the maritime incident as "concerning and regrettable" and called for efforts to shed light on what exactly happened, the semi-official Tasnim News reported.
Oil rebounds from five-week low as US issues warning to IranTensions are rising between the US and Iran after the Trump administration earlier this month ended exceptions to US sanctions on Iranian oil sales.
Asked what Iran should be worried the US might do, the president said: "You can figure it out yourself. They know what I mean".