The Brazilian model Gisele Bündchen has rebutted an extraordinary attack by Brazil’s agriculture minister, who called her a “bad Brazilian” for her environmental activism and said she did not know “the facts”.

Bündchen said the “bad Brazilians” were those responsible for Brazil’s worst deforestation figures in a decade.

In a letter addressed to the minister, Tereza Cristina Dias, published in Brazilian media, Bündchen lamented government figures showing deforestation had increased by more than 13% in a year.

“An immeasurable heritage threatened by illegal deforestation and the squatting of public lands. These, yes, are the ‘bad Brazilians’,” she wrote.

In a tweet, she said: “Since 2006 I have been supporting projects and getting involved in socio-environmental causes”. In the letter she said that her grandparents were farmers, so she understood the importance of agriculture to Brazil.

The war of words has highlighted rising international concern over the future of the Brazilian Amazon under the government of the far-right president, Jair Bolsonaro.

Bolsonaro has attacked the “fines industry” of environmental protection agencies. His foreign minister, Ernesto Araújo, regards global warming as a Marxist plot. And the environment minister, Ricardo Salles, this week suspended contracts with non-government bodies for 90 days and promised surprise visits to check what they were doing with government money.

In 2017, Bündchen criticised Brazil’s then president, Michel Temer, over plans to remove protected status for a large area of the Amazon – a move Temer later revoked. Last November she tweeted her opposition to Bolsonaro’s plans to fuse the environment and agriculture ministries – an idea that, along with withdrawing Brazil from the Paris climate deal, he later gave up on.

Dias made her comments in a radio interview on Monday. Bündchen countered Dias’s accusation that she did not know “the facts”, pointing out in the letter that she had been to the Amazon, was a United Nations environment goodwill ambassador and had taken part in the launch of the Global Environment Pact at the UN general assembly in 2017 at the invitation of the French president, Emmanuel Macron.

She said she had “participated in countless meetings with corporate presidents, universities, scientists, researchers, farmers and environmental organisations, where I was able to exchange information and learn more and more about how to take care of our planet”.

She said technology and scientific advances had to be used in favour of agriculture and to prevent deforestation from going past a point of no control.

“I see the preservation of nature not only as a legal environmental duty but also as a way to ensure water, biodiversity and climatic conditions essential for agricultural production,” she wrote. “I hope that during your mandate, concrete actions that result in a more sustainable, prosperous and just Brazil can be celebrated.”

Dias thanked the model for her “kindness” and said she would invite her to take part in a “positive agenda that brings agriculture and preservation together”.