(CNN)-- US President Donald Trump on Tuesday commented on the announcement by the Iran-backed Yemeni Houthi group of a ban on Saudi ship movement in the Red Sea, downplaying the threat.

Trump said in remarks to reporters: "If something like that happens, we will have to deal with the situation."

He added from the Oval Office: "So far, that hasn't happened. It could happen, but we handle things. We've done that with the Houthis before and haven't seen anything from them for a while."

Imposing a naval blockade on the Red Sea could open a new front in America's war with Iran, further tightening the flow of oil from the Middle East.

The Houthis warned Saudi ships against using the Red Sea in a message broadcast Monday to vessels operating in this vital waterway.

That has already affected shipping traffic and raised concerns among companies, a risk manager at a Fortune 500 company told CNN earlier Tuesday.

Trump declined to elaborate on the US response if the Houthis seek to close the waterway, merely referring to previous strikes against the group.

He said: "We carried out strong military operations against the Houthis for about 45 days, and we had no problem with them. And they had no problem with us for a long time, including during this conflict."