In separate interviews, with North Korean minders present, the two South Korean men said they admitted to the allegations against them.
The men, whose detention was announced in March
, said they had not been told what to say in the interviews. But they both made many of the same points, and their accounts were similar to a North Korean state media report from March about their cases.
South Korea has acknowledged that the two prisoners -- Kim Kuk-gi and Choe Chun-gil -- are its citizens, describing their detention as "deeply regrettable" and calling for their release.
The South Korean National Intelligence Service in March denied the allegations that the men were spying for it. An NIS official repeated Sunday that the accusations were "groundless."
Tales of espionage
In different rooms of a Pyongyang hotel on Sunday, the two men gave CNN accounts of the activities they are alleged to have carried out for the NIS.
CNN hasn't been able to independently verify their accounts. North Korea is often accused to push detainees to make false confessions.
Choe, 56, said he was working as a businessman in northern China, which borders North Korea, when he was approached by the NIS to gather information and materials from North Korea.
He said he worked as a spy for three years before he was detained near the border with China while trying to obtain several boxes of materials from inside North Korea. He said one of the boxes contained had material that could be used in military applications. He declined to be more specific.
Kim, 61, said he was a missionary struggling financially in northern China when the NIS recruited him, offering to pay for information about North Korea. The type of information they sought, he said, included itineraries of visits by leaders to foreign countries and copies of new North Korean currency to be used in forgery.
Kim said he earned about $500,000 over roughly nine years from the work before he was arrested as he attempted to gain information from an informant.
Praise for Kim Jong Un
The two South Korean men both said they are being kept in a place that isn't a prison but that belongs to the agency that is investigating them. They said they were being treated well.
They said that they hadn't been tried yet but that they would accept any punishment the North Korean government decided.
The men complained the South Korean government was disowning them.
Choe occasionally became emotional during the interview, especially when talking about his family. He said he has a wife and daughter in China and another daughter in South Korea.
He said he apologizes to his family for getting into trouble.
Kim said he had no family. But he warned other South Koreans not to do as he had done. He also talked about North Korean leader Kim Jong Un in glowing terms.
Other South Koreans held
North Korea, considered to be one of the most repressive regimes on earth, has an opaque justice system and a track record of false confessions.
Merrill Newman, an American veteran of the Korean War detained by North Korea in 2013, said that he was made to deliver an "apology" on state media that was not his own words.
Choe and Kim's interviews with CNN took place the day after North Korea said it had detained a South Korean man
who lives in New Jersey after he illegally crossed into its territory.
Another South Korean, Kim Jung-wook, was sentenced by a North Korean court last year to hard labor for life
after being convicted of committing "hostile acts" against the country.
The South Korean government tried to send a written notice to North Korea in late March about its detained citizens, but North Korea refused to accept it, said Lim Byeong-cheol, a spokesman for the Unification Ministry.
Lim told a regular news briefing Monday that South Korea is continuing to push for the release of the detainees through international organizations, governments with representatives in both Koreas and "other negotiating channels."