The Iranian drill and the arrival of the USS Gerald R Ford aircraft carrier near the mouth of the Mediterranean Sea underscore the tensions between the nations.
Iran earlier this week also launched a drill that involved live-fire in the Strait of Hormuz, the narrow opening of the Persian Gulf through which a fifth of the world's traded oil passes.
The movements of additional American warships and airplanes do not guarantee a US strike on Iran - but it does give President Donald Trump the ability to carry out one should he choose to do so.
He has held off on striking Iran after setting red lines over the killing of peaceful protesters and Tehran holding mass executions, while re-engaging Tehran in nuclear talks earlier disrupted by the Iran-Israel war in June.
"Should Iran decide not to make a Deal, it may be necessary for the United States to use Diego Garcia, and the Airfield located in Fairford, in order to eradicate a potential attack by a highly unstable and dangerous Regime," Trump wrote on his Truth Social website, seeking to pressure the United Kingdom over its plans to settle the future of the Chagos Islands with Mauritius.
Iran struggles with unrest at home following its crackdown on protests, with mourners now holding ceremonies honouring their dead 40 days after their killing by security forces.
Some of the gatherings have included anti-government cries, despite threats from authorities.
The drill on Thursday involved Iranian forces and Russian sailors conducting operations in the Gulf of Oman and the Indian Ocean.
The drill would be aimed at "upgrading operational co-ordination as well as exchange of military experiences", Iran's state-run IRNA news agency reported.
China had joined the "Security Belt" drill in previous years, but there was no acknowledgement it participated in this round.
In recent days, a vessel that appeared to be a Steregushchiy-class Russian corvette had been seen at a military port in the Iranian city of Bandar Abbas.
Iran also issued a rocket-fire warning to pilots in the region, suggesting they planned to launch anti-ship missiles in the exercise.
Tracking data showed the Ford off the coast of Morocco in the Atlantic Ocean at midday on Wednesday, meaning the carrier could transit through Gibraltar and potentially station in the eastern Mediterranean with its supporting guided-missile destroyers.
Having the carrier there could allow American forces to have extra aircraft and anti-missile power to potentially protect Israel and Jordan should a conflict break out with Iran.
The US similarly placed warships there during the Israel-Hamas war in the Gaza Strip to protect against Iranian fire.
In Iran, mourning ceremonies for those killed by security forces in the protests in January have increased.
Iranians traditionally mark the death of a loved one 40 days after the loss.
Witnesses and social media videos showed memorials taking place at Tehran's massive Behesht-e Zahra cemetery.
The demonstrations began on December 28 at Tehran's historic Grand Bazaar, initially over the collapse of Iran's currency, then spread across the country.
Tensions exploded on January 8, with demonstrations called for by Iran's exiled crown prince, Reza Pahlavi.
Iran's government has offered only one death toll for the violence, with 3117 people killed, while the US-based Human Rights Activists News Agency puts the toll at more than 7000.
