China continues to claim Taiwan as its own territory, and it has condemned the U.S. from communicating with Taiwan.
Chinese President Xi Jinping and Russian President Vladimir Putin released a joint statement saying there are "no limits" to the two countries' bond.
A Chinese official said the drills were provoked by "Taiwan's independence forces" and "external forces."
U.S. Navy Captain Mike Kafka said the Russian vessels had left the area following drills in the Pacific.
Contact with the German-made vessel was lost at 4:30 a.m. local time Wednesday, according to Indonesian military chief Hadi Tjahjanto.
Pyongyang warned that the planned aerial drill will "throw a wet blanket" on struggling negotiations.
Tensions in the Pacific run high between the U.S. and China over the independence of Taiwan and territorial claims in the South China Sea.
China's militarization of its island bases signified Beijing's determination to assert its territorial claims, regardless of U.S. opposition.
The training is held every year as part of the Foul Eagle joint military drills.
Nearly 7,000 U.S. troops are taking part in the 37th Cobra Gold drills held in Thailand.
"We are standing by and on guard 24 hours a day," said Lieutenant General Huang Kai-sen.
The drills come as the two allies clash over the controversial "comfort women" deal.
China carried out 16 drills near Taiwan in the past year prompting Taipei to warn that China's military threat was growing by the day.
Ultimately, President Jae-in believes that any possible stalemate rests upon Kim Jong Un.
More than 400 marines have been doing training activities together, including shirtless wrestling in the snow.
The exercise by China and Russia started the same day that the U.S., South Korea and Japan practiced underwater.
"We're ready to talk any time they'd like to talk," Tillerson said.
The aircraft left its base in the U.S. territory of Guam before joining two Japanese F-15 fighters to take part in the drills.
The air forces have begun five days of drills.
The drills are scheduled to take place November 11-14.
The largest U.S. warship in Asia, the USS Ronald Reagan, will join the USS Nimitz and the USS Theodore Roosevelt in the naval exercise next week.
President Donald Trump said North Korean ruler Kim Jong Un was "needlessly" threatening the lives of millions of people.
The drill aims to prepare the U.S. Forces Korea for an evacuation involving the families and pets of around 28,500 troops.
South Korea said the exercises would be the largest ever following the North's nuclear and rocket tests.
The move is part of Russia's large scale armed drills due to end tomorrow.
The move is part of ongoing military combat readiness drills.