The Korean Central News Agency (KCNA) said Kim had received the message from Assad yesterday.
In it, the Syrian president extended his "sincere congratulations" to Kim and "the friendly people" of his country 65 years after the establishment of the Democratic People's Republic of Korea, the North's formal name, according to KCNA.
The report said Assad also reconfirmed Syria's efforts to strengthen the "friendly and cooperative" relations between Syria and North Korea.
"We believe there has been a chemical weapons connection between North Korea and Syria," Defence Ministry spokesman Kim Min-Seok told reporters yesterday.
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The report also came as 11 of the nations attending the G20 summit in St Petersburg in Russia today called for a "strong" response to a chemical weapons attack in Syria blamed on the Assad regime.
US President Barack Obama argued at the end of the summit today that the world cannot "stand idly by" after the chemical weapons attack outside Damascus last month which the US claims was launched by Assad's regime.
However Obama and Russian counterpart Vladimir Putin failed today to end their bitter dispute over US plans for military action in Syria.
Any link between North Korea and the attacks in Syria could further isolate Pyongyang, which is prohibited from international sales of its weapons under UN sanctions for conducting nuclear and missile tests.
Suspicions over chemical weapons trade between Pyongyang and Damascus have been raised in the past.
South Korea supports international sanctions against Syria because the regime's use of chemical weapons, if confirmed, could give the wrong signal to North Korea, he said.