Ms Marin, who is married and has a four-year-old daughter, was said to have danced with three different men
The 36-year-old married mother-of-one is seen in new footage that has been shared widely on social media in Klubi night club at around 4am on August 7 with her arms around the man.
According to Finnish media the man is the famous singer-songwriter Olavi Uusivirta who is seen bringing his face close to Mrs Marin's neck and holding his hand in the small of her back as they share an intimate dance.
The day before Ms Marin denied doing anything illegal after videos taken earlier the same evening showed her dancing with friends inside a house while someone in the background yells 'flour gang'.
'Flour' is Finnish slang often used to refer to cocaine but Ms Marin said she had no idea why someone had shouted the term.
Ms Marin, who is married and has a four-year-old daughter, was said to have danced with three different men and then sat in the laps of two male companions, according to witnesses
Witnesses who were at Klubi when Ms Marin and her entourage rolled up around 2.30am on Sunday told Finnish outlet Seiska that she was dancing with “several” men an then then sat in the laps of two male companions.
Those with her were said to include Finnish singer-songwriter Alma and TikTok influencer Sabina Sarkka.
One witness said: “Sanna danced intimately with at least three different men.
“She also sat on the laps of two different men. She placed her hand next to one man and he held her gently by the arm.”
Another added: “My friends and I wondered if she is really still married. The ring still seemed to be there.”
Seiska added that Ms Marin had stayed in the club until at least 4.30am before going home to recover.
She then did a number of press interviews on the Monday morning during which her voice was noticeably hoarse.
Speaking from the Finnish capital Helsinki today, Ms Marin said she had taken a drug test, and expects the results next week.
The prime minister repeated her denials that she has ever taken drugs.
"I did nothing illegal," she told reporters in Helsinki.
"Even in my teenage years I have not used any kind of drugs," Ms Marin said, adding that she took the drug test as an added measure to allay any concerns.
The prime minister also insisted that she is entitled to the presumption of innocence.
Answering reporters’ questions whether she would have been able to make snap governmental decisions if necessary, she replied: “I don't remember a single time that there was a sudden situation in the middle of the night to go to the State Council Palace," she insisted.
"I think my ability to function was really good. There were no known meetings on the days I was partying."
Although Ms Marin acknowledged she was constantly being filmed, she said she was upset that the footage had become public.
"I trust that people understand that leisure time and work time can be separated," she added.
Formerly the world's youngest head of government - a title now held by Chilean President Gabriel Boric - Ms Marin makes no secret of partying, and has often been photographed at music festivals.
Just last week, Ms Marin was dubbed the "coolest prime minister in the world" by German news outlet Bild.
Two separate videos have emerged where the Finnish leader can be seen partying.
The first video, which emerged on Thursday, sparked the initial backlash against Ms Marin.
In the footage - thought to be taken from social media - she and Finnish celebrities are seen dancing and singing in a private apartment.
The Finnish leader held a news conference in response to the second video which emerged on Friday, where she can be seen dancing closely with popstar, Olavi Uusivirta.
A reporter claimed the popstar kissed Marin on the neck, the prime minister denied being kissed on the neck.
"I don't think I've been kissed on the neck. Something was said to me. I've hugged friends and kissed on the cheek. If it's considered inappropriate, then it's considered inappropriate," she added.
"If someone has kissed me on the cheek, there's nothing inappropriate or something I can't handle tell my husband," says Ms Marin.
There has been widespread reporting on the videos in local media and has prompted fierce debate in Finland about the way politicians handle themselves and the amount of privacy afforded to them.
Last year she apologised for going clubbing after coming into close contact with a Covid-19 case.