The North Korean leader expressed ‘great satisfaction’ over the drills, state media said.
Prosecutors in Malaysia had dropped a murder charge against Doan Thi Huong who is expected to return to Vietnam.
Putin offered to share details of his and Kim Jong-un's meeting with the US - to try to break the deadlock over nuclear weapons.
Vladimir Putin and Kim Jong-un have been holding talks over how to defuse a standoff over Pyongyang's nuclear programme.
The secretive leader left Pyongyang by his special train at dawn on Wednesday.
The test comes during an apparent deadlock in nuclear disarmament talks with the United States.
The marathon is part of celebrations to mark the anniversary of North Korea founder Kim Il Sung's birth in 1912.
She has been sentenced to three years and four months from the day she was arrested in February 2017.
The singer belted out some of her songs to a crowd in Pyongyang.
White House press secretary Sarah Sanders said the two leaders had a "very good and constructive meeting".