MANAMA, Bahrain — The commander of the Navy’s Fifth Fleet was in his office on the afternoon of July 25 when he got the phone call: An Iranian Navy frigate in the Gulf of Aden had approached a ship where an American military helicopter had just landed.

Crew members on the Iranian ship pointed a heavy machine gun at the American helicopter, an alarming provocation at a time when critics are trying to kill a nuclear deal limiting Iran’s nuclear program in exchange for sanctions relief. The American helicopter, following standing orders to defuse tensions instead of elevating them, took off from the ship, but the Iranian crew continued to track it with the gun for a few moments before turning away.

Then the report took a strange turn. During the entire episode, Vice Adm. John W. Miller, the Fifth Fleet commander, was told that an Iranian film crew aboard the frigate was videotaping everything. “The whole thing took a couple of minutes,” Admiral Miller said later, recounting his surprise at the film crew. “We have no idea why they were filming it.”

But wait, how did the Navy know the Iranians were filming the episode?

Admiral Miller burst out laughing. “Well, because we were filming them,” he said. “We have our video of their video.”In the crystalline waters of the Arabian Sea, it is spy versus spy between the United States and Iran. Ever since the United States, Iran and other world powers signed a pact to rein in Tehran’s nuclear ambitions, skeptics of the deal — which is subject to congressional approval — have feared that the United States and Iran, longstanding regional adversaries, might let up on decades of vigilance.

But in the skies and waters of the Persian Gulf, the Strait of Hormuz, the Arabian Sea and the Gulf of Aden, the two continue to constantly watch each other. American naval ships openly roam the waters along Iran’s 1,100-mile-long southern coastline, their radar trained on the Iranian shore and on Iranian ships leaving their harbors. Iranian fighter jets patrol the skies, keeping an eye on American combat planes that take off from an aircraft carrier in the Persian Gulf every time an Iranian jet comes close to their ship.

“It’s a little bit of a game we play,” said Capt. Benjamin Hewlett, the commander of the air wing aboard the aircraft carrier Theodore Roosevelt, which is in the Persian Gulf keeping an eye on Iran right now. “When they launch, we launch. We consider this our sovereign territory, so we make sure they’re not unescorted in and around the aircraft carrier.”

Sometimes it seems like a game of chicken — only with risks so high that a single misstep could unravel what has been a tenuous standoff between the United States and Iran for 36 years.

But for the Obama administration, the American naval presence off Iranian shores is now more important than ever as the administration seeks to assure Middle Eastern allies and a skeptical Congress that the United States will continue to keep an eye on Iran.

Aboard the Theodore Roosevelt, a steady stream of military officials from the region have arrived to see the situation for themselves. A few weeks ago the Saudi defense minister, Deputy Crown Prince Mohammed bin Salman bin Abdulaziz al-Saud, got a standard tour of the flight deck and viewings of fighter jets screaming into the air, but Navy officials also took him into the combat direction center, a classified room deep in the carrier where operations specialists track Iran using an array of high-tech equipment.

Officers on the Roosevelt said there was less Iranian activity in the gulf in the weeks leading up to the conclusion of the nuclear deal in July, but all the officers said the slowdown was most likely because of Ramadan. After the deal was signed — and Ramadan ended — the officers said Iranian activity in the gulf picked up as Iran deployed more warships off the Iranian coast and increased its fighter jet flights.

“I don’t think things are any different now than they were before” the nuclear pact was signed, Rear Adm. Roy Kelley, the commander of the strike group aboard the Theodore Roosevelt, said in an interview on the ship’s bridge. “We have interactions every day with Iran. Fifty percent of the Persian Gulf coastline is Iran, so when they see us here, they come and check us out.”

He added that “for the most part, they’re professional.”

A few minutes later, an announcement sounded throughout the aircraft carrier: “Gun Quarters....Set Conditions Thunder” — something unknown was nearing the carrier, which, Captain Hewlett said, usually means an Iranian ship or aircraft.

It was in fact an Iranian ship, but it did not get close, and soon there was the all clear.

The constant watchfulness can make for heightened nerves. In April, just two days after the Roosevelt arrived in the Persian Gulf to relieve the aircraft carrier Carl Vinson, military officials ordered the ship to turn around and head to the waters off the coast of Yemen to block an Iranian convoy suspected of transporting weapons to Houthi fighters there. The Roosevelt, escorted by the guided missile cruiser Normandy, was soon passing through the Strait of Hormuz into the Arabian Sea and then south to the Arabian Peninsula.

On board, sailors realized that the world was watching to see who would blink first. “Us arriving and then turning around so soon was unusual,” said Cmdr. Andrew Strickland, the head of the Combat Direction Center on the Roosevelt. In the combat center, where much of the time is spent watching Iran, suddenly tactical officers were watching themselves — on television news reports about the drama unfolding as the Roosevelt moved to block the Iranian convoy. “It was definitely weird to suddenly be seeing your own ship on CNN,” said Lt. William Thomas, a tactical action officer who works in the combat center.

For the Obama administration, it was important to signal to skeptics that even though the United States was in the final stages of negotiating the nuclear deal with Iran, the administration would continue to back its regional allies against Iran — particularly Saudi Arabia, which was in the middle of a bombing campaign against the Houthis in Yemen that Saudi officials said was necessary to try to restore the ousted American-backed Yemeni government.

Things on the ship “were a little more tense,” Captain Hewlett said. “It’s a big political message for our country to send to their country.”

At the time, one Pentagon official compared the decision to deploy an aircraft carrier to turn around a weapons convoy as similar to deploying a nuclear weapon to kill an ant.

To the surprise of almost no one, the Iranian convoy, within two days of the arrival of the Roosevelt, turned around and headed back toward Iran.

This article was written by Helene Cooper for the New York Times on Aug. 17, 2015.