A source with direct knowledge of the message told Reuters it's an effort by North Korea to force the United States into diplomatic talks with Pyongyang.
The source says the further nuclear tests could also be accompanied by another rocket launch this year.
The isolated regime conducted its third nuclear test on Tuesday, drawing global condemnation.
South Korea has responded to the test by conducting extensive combat drills near the North Korean border.
"It's all ready. A fourth and fifth nuclear test and a rocket launch could be conducted soon, possibly this year," the source said, adding that the fourth nuclear test would be much larger than the third at an equivalent of 10 kilotons of TNT.
The tests will be undertaken, the source said, unless Washington holds talks with North Korea and abandons its policy of what Pyongyang sees as attempts at regime change.
North Korea also reiterated its long-standing desire for the United States to sign a final peace agreement with it and establish diplomatic relations, he said.
The North remains technically at war with both the United States and South Korea after the Korean war ended in 1953 with a truce.
Initial estimates of this week's test from South Korea's military put its yield at the equivalent of 6-7 kilotons, although a final assessment of yield and what material was used in the explosion may be weeks away.