The G7 aid offer was announced by French President Emmanuel Macron on Monday.
Rejecting the aid, Bolsonaro on late Monday said Brazil was not a "colonial territory" and that there was "a hidden agenda" behind Macron's offer.
Bolsonaro's Defence Minister said the fires in the Amazon were "not out of control". Commenting on the G7 offer of aid, Bolsonaro's Chief of Staff Onyx Lorenzoni told the Globo news website: "Thanks, but maybe those resources are more relevant to reforest Europe."
"Macron cannot even avoid a predictable fire in a church that is part of the world's heritage, and he wants to give us lessons for our country?" Lorenzoni added, in a reference to the fire that hit Notre-Dame cathedral in Paris in April.
Brazil's Foreign Minister Ernesto Araujo tweeted on Monday: "No one needs a 'new initiative for the Amazon' as Macron suggests when there are already several mechanisms under the UN Climate Convention to fund the fight against deforestation."
In a joint news conference Monday with Chilean President Sebastian Pinera, Macron announced that G7 countries would allocate $22 million in emergency funding to help with efforts to prevent fires in the Amazon rainforest. He also said France would provide military support in the region to fight the fires.
A record number of fires are burning in Brazil, mostly in the Amazon, according to the country's space research agency, Inpe. Macron last week described the fires as an "international crisis" and called for an emergency meeting of G7 countries regarding the fires.
In an interview with French public broadcaster France 2 at the conclusion of the G7 summit in Biarritz, Macron said Bolsonaro's attitude towards deforestation could derail ratification of the free trade agreement between the EU and the Mercosur group.
"We respect your sovereignty. It's your country," said Macron, before insisting that the Amazon fires are a global issue.
"The Amazon forest is a subject for the whole planet We cannot allow you to destroy everything," he added.
In response to this, the Brazilian Foreign Minister said: "The efforts made by some political currents to extrapolate real environmental issues by transforming them into a fabricated 'crisis' as a pretext for introducing mechanisms for external control of the Amazon are very evident.
"Brazil will not accept any initiative that involves relativizing sovereignty over its territory, whatever the pretext and whatever the guise."
The Brazilian armed forces, deployed by Bolsonaro in the fight against the fires, are reportedly operating in eight of the nine Amazon states.
The mobilization of the troops was announced on August 23 by Bolsonaro as the first measure to fight fires amid strong condemnation he has received for the government's lack of action against illegal deforestation of the Amazon.
( With inputs from IANS )