A memo signed by all members of the Joint Chiefs of Staff also reminded military members that Joe Biden was duly elected as the next president and will be sworn in to office on Jan. 20.
The Navy said the Arleigh Burke-class guided missile destroyers USS John S.McCain and USS Curtis Wilbur "conducted a routine Taiwan Strait transit" in accordance with international law.
This was the first time that four big democratic nations — the US, Japan, Australia and India — termed as Quad got together for the exercise.
The mega exercise is taking place at a time India and China are locked in a nearly six-month-long bitter border standoff in eastern Ladakh.
The Indian Navy had a few years ago expressed interest in the acquisition of 57 naval fighter aircraft for operations from its aircraft carriers.
The invitation by India to the Australian Navy for the exercise next month came two weeks after the foreign ministers of the Quad held extensive talks in Tokyo.
The US and Japan are the other countries that participate in the annual exercise, which is likely to take place next month in the Bay of Bengal and Arabian Sea
In 2016, India and the US inked the Logistics Exchange Memorandum of Agreement (LEMOA) that allows their militaries use each other's bases for repair and replenishment of supplies.
China in the recent years has increased its maritime operations in the IOR with a deployment of around eight warships on anti-piracy mission.
It was proving to be a stubborn blaze to put out, requiring helicopters dumping water from above, firefighting vessels shooting seawater and fire trucks pounding water through hoses from the dock.
The Guard launched Iran's first military satellite Wednesday, unveiling a previously secret space program.
A week ago, 11 small armed Iranian Revolutionary Guards Corps speedboats swarmed around US Navy and Coast Guard ships in international waters in the northern Gulf.
The incident Wednesday saw the US Navy release video of small Iranian fast boats coming close to American warships as they operated in the northern Persian Gulf near Kuwait.
Captain Brett Crozier's COVID-19 test result was reported Sunday by the New York Times, just hours after US Defense Secretary Mark Esper defended the captain's firing.
Although the Navy is much smaller than the Army, it accounts for at least one-third of all reported COVID-19 cases in the military.