"Personally, I see some big problems and today I told Petraitis that, in my opinion, the best option would be for him to resign from his position," Dulkys told reporters after meeting with the director.
"I was asked to give (him) time to think it over. So we agreed that I would wait for that answer until Monday morning," he added.
"I have given it a lot of thought and I am stressing today that the organization has seen all kinds of internal stories and situations throughout its existence and especially during the crisis, but I think we have reached a point where we just need to cut the Gordian knot," Dulkys said.
"We don't have time. There's a crisis and we need well-functioning organizations," he added.
If Petraitis refuses to resign, Dulkys will have "to look for another way" and take "more bureaucratic action".
The call on the director to step down comes after it emerged that hundreds of coronavirus-related deaths had not been included into the official statistics.
The minister met with Petraitis last Tuesday to discuss the situation, but said that he was not convinced by the director's answers and asked him to submit them in writing.
Prime Minister Ingrida Simonyte has called on the NPHC heads to take responsibility.
Petraitis told a press conference on Sunday that there were 1,171 unaccounted for deaths, but said it was due to hospitals' failure to provide the center with information in a timely manner.