Although Mr. Jackson may have broken new political ground in the mayor’s race, it was not the first time he has exercised his power with the country’s politicians.

In March, The New Zealand Herald reported that Mr. Jackson had called a meeting with Jacinda Ardern, New Zealand’s prime minister, after he heard that she was considering cutting government subsidies for the film industry.

Although officials had said that the subsidies did not provide value for the money to taxpayers, Ms. Ardern’s center-left government ultimately decided to leave them untouched. The government said the move was not related to Mr. Jackson.

In 2010, he was at the heart of a dispute in which Warner Bros. threatened to move production of his “Hobbit” films away from New Zealand unless the government supported changes to employment laws. The fight pitted Mr. Jackson against the actors’ unions, which said the changes would revoke performers’ rights.

The center-right government at the time sided with Warner Bros. and Mr. Jackson.

Mr. Jackson, a soft-spoken man with a relaxed appearance — he is known to go barefoot, like the hobbits of J.R.R. Tolkien’s books — has won three Academy Awards, and his films have grossed more than $2 billion. His movies set in New Zealand are credited with luring visitors to see the country’s natural beauty for themselves, a boon that tourism officials said was worth tens of millions of dollars a year.

“Peter is a very, very big fish in quite a small tank,” a former prime minister, John Key, told The New York Times in 2012.

Mr. Jackson has accumulated particular clout in Wellington, where he has invested in philanthropic projects and hosted world premieres of his films.