Trump said last week that the United States was withdrawing from a 2015 deal negotiated by the Obama administration.
The withdrawal has upset Washington’s European allies, cast uncertainty over global oil supplies and raised the risk of conflict in the Middle East.
"It is a period of uncertainty that we are entering into right, how the whole world will respond to this latest development," Chief of US Naval Operations Admiral John Richardson told a small group of reporters.
"(We have to) remain alert, I mean even a little bit more alert than usual to just be open to any kind of response or new development or something like that," Richardson added.
He was speaking after visiting the aircraft carrier George H.W. Bush off the coast of Virginia where US and French troops are carrying out joint training.
Richardson said the US Navy had not seen provocative Iranian behavior in the Gulf since Trump's announcement, but was watching closely.
In recent years, there have been periodic confrontations between the Islamic Revolutionary Guard Corps (IRGC), a branch of Iran's armed forces, and US military in the Gulf - a major trade route for oil - but there have been no major incidents since last year.
Last August, US officials said an Iranian drone came within 100 feet (30 meters) of a US Navy warplane as it prepared to land on an aircraft carrier in the Gulf.
Iran, which sees the Gulf as its backyard and believes it has a legitimate interest in expanding its influence there, has long argued that the region should organize its own security collectively, without outside powers.
