The 24-year-old man, identified by police as a Japanese national who travelled frequently in and out Thailand, has not been charged.
His Thai lawyer, Kong Suriyamonthon, said his client wants to clear up the allegations against him.
"It's a DNA sample, yes. He wants the truth to be known," Mr Kong told reporters on Monday, adding that he did not know whether his client would return to Thailand.
He declined to confirm his client's whereabouts but said the DNA samples had come from Japan.
Pol Col Naiyawat Padermchit said at least 12 babies tested were fathered by the same man.
Thailand has been gripped by surrogacy scandals in recent weeks following allegations that an Australian couple had abandoned their Down Syndrome baby with his Thai birth mother taking only his twin sister back to Australia with them.
Earlier this month, Thai police discovered nine surrogate babies with their nannies and a pregnant surrogate mother at a Bangkok apartment, dubbed the "baby factory" by media. Police later said they had found more babies, all suspected of being fathered by the Japanese businessman.
"We have intelligence that he is a rich man and his father gave him a lot of money. We also know he took children from Thailand to Cambodia," Thailand's Interpol director, Apichart Suriboonya, told Reuters, adding that police had found no link to human trafficking.
Thailand's military government, which took power in May, has given preliminary approval for a draft law to make commercial surrogacy a criminal offence.