Radio Free Asia, a US-funded non-profit broadcaster, said in a Korean language dispatch monitored in Seoul that the men, who claimed to be North Korean, entered the embassy compound in the Laotian capital on Friday.
The broadcaster, citing the embassy spokesperson, said the Swedish government was in talks with relevant states about what to do next.
But the spokesperson refused to give details of the men’s identities and at which country they wanted to eventually take refugee.
Tens of thousands of North Koreans escape to China and often move on to Mongolia or Southeast Asia to try and secure safe passage to South Korea, as Beijing returns any refugees it catches as economic migrants.
The number of North Koreans who had made it to South Korea since the end of the 1950-53 war topped 10,000 in February.