Opposition politicians have questioned her priorities and at least one called for her to take a drugs test.
Ms Marin, who at 36 is the world’s youngest national leader, admitted she had been exuberant but insisted she not used drugs.
“I danced, sang, and partied — perfectly legal things,” she said. "And I've never been in a situation where I've seen or known of others [using drugs].
“I have a family life, I have a work life and I have free time to spend with my friends. Pretty much the same as many people my age.”
She said she knew she was being filmed and was upset that it was made public.
“I am going to be exactly the same person as I have been until now and I hope that it will be accepted,” she said.
Opposition leader Riikka Purra demanded Ms Marin take a voluntary drug test. Others criticised her and the media for talking about the parties instead of policies.
Ms Marin has made no secret of her parties and has previously been filmed at music festivals.
“The reaction is very typical on all things Marin: polarised,” Finnish political journalist Robert Sundman told the BBC.
“There are people saying that it is normal for a woman her age to have fun with her friends — and people who are shocked.
“But at least until now one thing is sure: the previous party pictures have not — at least significantly — affected popularity of her or her party."
Ms Marin has been in power since December 2019, when Finland’s ruling Social Democratic Party council voted 32-29 for her to take over the top governmental post from Antti Rinne.
A parliamentarian since 2015, she has been the party's vice chairwoman and served as minister for transport and communications.
Finland applied to join Nato under her leadership after the invasion of Ukraine. Finland and Russia share a 1,340km border.
Ms Marin is said to retain the support of her party.