The scheduled drills, involving a US nuclear submarine, come after North Korea said it was planning to carry out its third test of a nuclear device.
The US and South Korea have promised “significant consequences” if it goes ahead with the underground explosion.
The North has criticised the naval drills as “war-mongering”.
The exercises, taking place off the east coast of the Korean peninsula, involve live fire, naval manoeuvres and submarine detection drills.
Officials have stressed they were planned before the latest rise in tensions.
But South Korea’s Joint Chiefs of Staff chairman Jung Seung-Jo said the presence of the nuclear-powered submarine USS San Francisco in the region “would itself serve as a message to North Korea”.
North Korea says its launch of a rocket in December was for the sole purpose of putting a satellite into orbit, but the US and North Korea’s neighbours say it was a test of long-range missile technology banned under UN resolutions.
After the UN Security Council voted to increase its sanctions against Pyongyang, it announced plans to carry out what it described as a “high level” nuclear test, aimed at it “arch enemy”, the US.
South Korean officials say they believe North Korea is now in the final stages of preparing for the test.
“We assess that North Korea has almost finished preparations for conducting a nuclear test any time and all that’s left is North Korea making a political decision,” defence ministry spokesman Kim Min-seok told reporters on Monday.
Satellite images have shown the tunnels which have been dug into the mountainside at the test site being sealed off, and camouflage netting being put in place.
On Sunday, North Korean leader Kim Jong-un held a high-level meeting at which he made what the country’s media said was a “historic” speech.
The meeting discussed “bringing about a great turn in bolstering military capability”, said the state news agency KCNA, without giving further details.
Meanwhile, diplomatic efforts are continuing to dissuade the North from going ahead.
As one his first acts on becoming the new US secretary of state, John Kerry spoke to his South Korean counterpart Kim Sung-hwan at the weekend.
In Beijing, South Korean nuclear envoy Lim Sung-nam met Chinese counterpart Wu Dawei and urged China to exert pressure on Pyongyang not to go ahead with the test, Yonhap news agency reported