China has lodged a formal protest after New Zealand’s top diplomat told a Chinese-born lawmaker to “go back to your own country,” a comment that has also prompted calls at home for the minister’s dismissal.

The foreign minister Winston Peters, leader of the populist New Zealand First party and a longtime political kingmaker in New Zealand, made the remarks during a heated debate in the Parliament in Wellington on Wednesday in a retort to Lawrence Xu-Nan, a Green Party lawmaker whose family had immigrated when he was a child.

Responding to a shouted question from Mr. Xu-Nan about whether he was vaccinated for Covid-19, Mr. Peters said: “I know you just came here five minutes ago. Go back to your own country, that’s where they lie like a flatfish. But they don’t lie like that here.”

The Chinese Embassy in New Zealand said in a statement that it had “lodged solemn representations,” a phrase Beijing uses to signal it has made a formal complaint or protest, with the country’s foreign ministry, saying members of the Chinese diaspora were well-integrated and “deserve to be recognized and respected.” New Zealanders of Chinese heritage make up about 5.6 percent of the population, according to the latest census.

Asked about Mr. Peters’s comments, Mao Ning, a spokeswoman for China’s foreign ministry, said, “It is hoped that relevant individual in New Zealand will do more things that contribute to the friendship between our two countries, and refrain from making China an issue in domestic politics.”

On Chinese social media, some people were angered by Mr. Peters’s remarks, which they called racist. But others dismissed Mr. Xu-Nan’s connection to China, as he is not a citizen.

Prime Minister Christopher Luxon of New Zealand called Mr. Peters’s comments “very offensive and completely inappropriate,” and when asked by a reporter whether he thought the comment was racist, said he did.

He nonetheless demurred on calls to fire him from an array of politicians, including a former prime minister, saying Mr. Peters, who is 81, was a successful foreign minister and that the decision was in the public’s hands with the general election three months away.

Mr. Luxon added that his party was focused on other priorities rather than “distractions and sideshows by populist politicians trying to bring attention to themselves.” Mr. Luxon’s National Party leads a coalition government with two smaller parties, including Mr. Peters’s New Zealand First.

Mr. Peters has refused to back down from or apologize for his comments, saying he was making the point that New Zealand was a democracy with free speech and rights.

“If that offends the pearl-clutchers and the communist shills labeling it as ‘dangerous’ — welcome to New Zealand,” he wrote in a social media post.

Mr. Peters is known for his brash rhetoric. He has previously made comments deriding or vilifying Asian immigrants and campaigned on lowering migration from Asia in the 1990s.

Mr. Xu-Nan, who the Green Party says is its first Chinese-born member of Parliament, told reporters after the parliamentary session that there needed to be accountability for “repeated behavior and racism from one particular member and a senior member” of Mr. Luxon’s cabinet.

Wang Xiaolong, China’s ambassador to New Zealand, said in a social media post: “Sometimes, a statement says more about the person that makes it than anything or anybody else.”

Berry Wang contributed reporting from Hong Kong.