Several New Zealanders were on board ships taking part in the flotilla, some of who were detained by Israel when nearing Gaza.
The flotilla involving more than 500 people, including Swedish climate campaigner Greta Thunberg, was trying to break Israel's blockade.
Videos from social media showed protesters outside Peters' home on Thursday.
Footage seen by RNZ shows people chanting, banging drums, waving Palestinian flags and holding posters.
Messages had been written on the footpath in chalk, including the names of some of the New Zealanders on the flotilla.
Police officers could also be seen.
Peters' office declined to comment.
Adi Leason, whose son Sam was among those detained, told RNZ's Midday Report they were immensely proud.
"I think Samuel has indicated that he is prepared to take his struggle and his witness to sort of another level and stay in jail as, I guess, a silent witness."
Police attend protest
A police spokesperson told RNZ that officers responded to a protest at 6:52pm on Thursday evening.
They said around 30 people had gathered outside an Auckland property and police staff monitored protest activity.
The spokesperson said Auckland Council noise control officers attended on two occasions and found noise levels had exceeded acceptable standards.
"The group lowered the noise levels on both occasions, before dispersing without further issue at around 10pm."
RNZ has had contact with three of the New Zealanders on board the flotilla.
Last month Youssef Sammour told Saturday Morning that he had been involved in two similar flotilla missions prior to being involved in the current event.
Sammour said he was hopeful that boats from the flotilla would make it to Gaza given how many people were involved.
He said that he was on a 42 foot sailing yacht with six others onboard.
Those people included an influencer, a journalist, a medic and an MP from Spain.
Sam Leason told Checkpoint last week that [https://www.rnz.co.nz/news/national/574010/kiwi-teen-sam-leason-describe...
boats that were part of the flotilla had been attacked by drones].
"I think nine boats got hit by bombs and other liquids ... flammable liquids. I think 12 different things were dropped on nine different boats. ...It was red alert, all crazy, it was a pretty scary time."
Leason said he was taking part in the flotilla because children were being bombed in Gaza and the New Zealand government wasn't doing enough to deter Israel.
He was scared but noted it did not compare to what Gazans were enduring on a daily basis.
The Sydney Morning Herald reported on Thursday that a New Zealand-born Melbourne-based GP named Bianca Webb-Pullman was sailing with the flotilla.
