South Korea says it has seen indications that the North is preparing more missile launches, possibly an intercontinental ballistic missile.
It said it was strengthening its controversial US-made Thaad missile defence system after the North’s test of a nuclear bomb at the weekend.
The South has carried out live-fire exercises in response to the test.
The US has warned that any threat to itself or its allies will be met with a “massive military response”.
The North says it tested a hydrogen bomb that can fit on to a long-range missile.
Pyongyang has repeatedly defied UN sanctions and international pressure by developing nuclear weapons and testing missiles, and the provocations have only intensified.
In the past two months it has conducted intercontinental ballistic missile tests, sending one over mainland Japan into the Pacific Ocean. It has also threatened to fire missiles towards the US Pacific territory of Guam.
The United Nations Security Council is to hold an emergency meeting later on Monday to discuss its response.