The announcement came from French President Emmanuel Macron, the host of this year's meeting of G-7 leaders, and the Chilean President Sebastián Piñera.
Brazil's powerful agriculture sector - which strongly supports Bolsonaro - has expressed concerns over the president's rhetoric, fearing boycotts of their products in key markets.
Bolsonaro has previously described rainforest protections as an obstacle to Brazil's economic development.
French President Emmanuel Macron has lashed out at Brazil's Jair Bolsonaro for endorsing "rude" remarks about his wife. "It's sad, it's sad first for him, as well as for Brazilians".
"We can not accept a president, Macron, launching unreasonable and gratuitous attacks on the Amazon, or masking his intentions behind the idea of an "alliance" of G7 countries to "save" the Amazon, as if we were a colony or a no-man's land", the far-right Brazilian leader tweeted. "Brazilian women are probably feeling ashamed of their president".
Asked if he would speak with Macron, Bolsonaro said Saturday, "If he calls me, I will answer".
G7 countries have agreed to an immediate $26.6 million to help Amazon countries fight wildfires and launch a long-term global initiative to protect the rainforest.
An official at Macron's office said the French leader had later explained his position to Merkel.
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Earlier this week, Bolsonaro, whose anti-environment rhetoric since coming to power in January has been blamed for harming the Amazon and indigenous tribes, accused non-governmental organizations of deliberately starting the fires after their funding was cut.
Two C-130 Hercules aircraft carrying thousands of liters of water on Sunday began dousing fires devouring chunks of the world's largest rainforest, which is seen as crucial to keeping climate change in check.
Brazilian farmers sometimes start fires at this time of the year to illegally clear land for livestock.
US President Donald Trump and British Prime Minister Boris Johnson, both attending the G7 summit, have offered their countries' assistance in fighting the fires.
Close to 80,000 fires have been registered across large swaths of the Amazon, the highest number since at least 2013, according to INPE.
Although about 60 percent of the Amazon is in Brazil, the vast forest also spreads over parts of eight other countries or territories.
His decision to appoint his son Eduardo Bolsonaro as Brazil's ambassador to the United States was considered wrong by 72.7 per cent of the people polled.
Almost 80,000 fires have been registered across Brazil through August 24, the highest since at least 2013, according to space research agency INPE. According to local news outlet Globo Rural (and as tweeted by investigative reporter Glenn Greenwald), the group told the federal government in advance of lighting the match, hoping that Bolsonaro's government would forgive the hefty fines that normally accompany environmental crimes.