Pyongyang has strongly condemned the exercises, threatening to scrap the armistice that ended the Korean War.
Seoul says North Korea also appears to have carried out a threat made last week to sever a cross-border hotline.
The drills come days after the UN approved new sanctions on North Korea following its nuclear test in February.
The test last month was the communist country’s third. It followed an apparently successful launch in December of a three-stage rocket, seen as a banned test of missile technology.
North Korea’s neighbors and the US fear it is working to build a nuclear warhead small enough to put on a missile, but believe it does not yet have the capabilities to do so.
The US-South Korea joint drills, which are known as “Key Resolve”, last two weeks and involve more than 13,000 troops. Another joint exercise, known as Foal Eagle, has been under way since the beginning of March.
Both exercises take place every year, usually prompting strong rhetoric from the North.
In apparent response to the UN sanctions vote, however, North Korea has issued multiple threats, promising to abandon the Korean War armistice, pull out of non-aggression pacts with North Korea and cut cross-border links, including the hotline.
Early on Monday, South Korea’s Unification Ministry said efforts to contact the North via the hotline had been unsuccessful. The hotline, installed in 1971, has been severed on five previous occasions.
North Korea also appears set to carry out its own military drills this week, South Korea says.
Late last week, South Korea’s new President, Park Geun-hye, warned that the security situation on the Korean Peninsula was “very grave”.
The two Koreas remain technically at war, because an armistice was signed at the end of the 1950-53 Korean conflict, rather than a peace deal.
Tensions have boiled over on a number of occasions in the past, most recently in November 2010 when four South Koreans were killed in North Korean shelling on a border island.
North Korea’s Communist Party newspaper, Rodong Sinmun, warned on Monday that the situation was unpredictable.
“With the ceasefire agreement blown apart… no one can predict what will happen in this land from now on,” the mouthpiece said.
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