(CNN) The director of the religious group at the center of South Korea's novel coronavirus outbreak has denied responsibility for the recent spike in infections, saying authorities were trying to "exaggerate" its involvement to shift blame.

Kim Shin-chang, director of international missions for the Shincheonji religious group , told CNN Sunday that members had been fully transparent and cooperative with authorities in trying to contain the outbreak.

The coronavirus, formally known as Covid-19, has infected 3,526 people and killed 17 in South Korea. Health authorities say more than half of all cases are related to Shincheonji -- an offshoot of Christianity -- and a specific branch in the southern city of Daegu.

South Korea's Ministry of Justice last week said that 42 Shincheonji members had traveled from Wuhan, the Chinese city where the coronavirus originated, to South Korea since July.

Many of the cases in other countries came from people who had traveled to Wuhan, or had been in contact with someone who had -- meaning the 42 members could have brought back the virus if they were traveling during the peak of the outbreak.

Kim told CNN there were 357 Shincheonji members based in Wuhan. He said that while the group didn't have official travel records for all its members, "we have no record" of any coming from Wuhan into South Korea since November.

He said the outbreak began in December -- so there was no need to check members' travel history from July.

"It makes me wonder if they are trying to exaggerate the link or possibly move the responsibility to Shincheonji," he said. "I would like to ask the Ministry of Justice why they did not check all Chinese and Korean citizens (traveling) from Wuhan since July, and why they only released the number of 42 (Shincheonji) members."

The Ministry of Justice said it had pulled the immigration records from July on request of the Korea Centers for Disease Control and Prevention (KCDC). CNN has reached out to KCDC for comment.

'We did our best in the situation'

After identifying and announcing the Shincheonji link on February 18, South Korean authorities raced to contain the spread of the virus, tracking down thousands of attendees to trace their contacts and symptoms. It took a week before the group gave a list of member's names to authorities.

About 600 Daegu police officers were deployed to knock on doors, track phones, and scour security camera footage to find them, as members often don't answer phone calls from nonmembers.

Daegu's mayor, Kwon Young-jin, said Friday that the group had also omitted some members in a list of attendees submitted to city authorities, and that he would report the group to police for "hampering the city's measures to contain the virus."

Kim apologized "to the Korean people for the worries we have caused" -- but insisted Shincheonji had been fully transparent.

"We shut down all offices to prevent further spread, and our administrative process has become delayed as all members are working from home so they can self-isolate themselves to the fullest extent," he said.

"I'm sure there have been areas where we could have done better but we do want to emphasize that we did our best in the situation."

Kim also admitted members had been encouraged to deny being part of the group — not to conceal any vital information or to hamper the coronavirus investigation, but because "Shincheonji is perceived as a cult, and because of this many members are discriminated against."

He dismissed other accusations too, like claims by former member Duhyen Kim that illness was never accepted as a valid reason to miss services.

In February, Duhyen Kim described to CNN how, when he was a member, followers would sit on the floor during hours-long services "packed together like sardines." He and several other former members described how attendees are not allowed to wear masks during prayer time, as it was seen as "disrespectful to God."

Shincheonji religious group event.

Such claims were outdated and inaccurate, said Kim Shin Chang, adding that since January, members with symptoms had been told not to come in, or to wear masks during service.

"So there is no evidence that our service method is the reason we are seeing such an outbreak in our group," he said.

What is Shincheonji, and how did the virus spread?

Shincheonji Church of Jesus, the Temple of the Tabernacle of the Testimony was established on March 14, 1984.

It was founded by Lee Man-hee, who is revered as a god-like figure within the group -- he is even believed to be "the second coming of Jesus Christ," said Duhyen Kim.

The virus is believed to have spread through cases who attended a Shincheonji service or were in contact with attendees, authorities say.

Between January 31 and February 2, an unknown number of members came together for the funeral of the founder's brother, who had been hospitalized near the southern city of Daegu.

Numerous confirmed coronavirus cases and deaths have since been recorded from the same hospital.

JUST WATCHED Inside South Korea's epicenter of the coronavirus outbreak Replay More Videos ... MUST WATCH Inside South Korea's epicenter of the coronavirus outbreak 02:56

Then, on February 18, South Korea reported its 31st case -- a 61-year-old woman with no prior overseas travel history or contact with other confirmed cases.

A cluster of infections followed. By February 20, the national tally had increased from 31 to 156 and the first death was reported.

While tracing the movements of the 31st patient, the South Korean Centers for Disease Control and Prevention spotted a link between the new patients: case number 31 had attended a Shincheonji service with hundreds others in Daegu.

Once the link to the religious group was established, authorities sprang into action, quarantining attendees, disinfecting buildings, and closing down the group's services.

Shincheonji members from the John tribe in Los Angeles.

The group says it has about 245,000 members in total, with more than 31,000 from overseas. An internal document from 2017, called the "International Missions Department status report," provided to CNN by former members, said the group has eight branches in the US, with the LA chapter being the largest with more than 1,000 members, as well as dozens of chapters in China.