France and Ireland say they will not ratify a huge trade deal with South American nations unless Brazil does more to fight fires in the Amazon.
French leader Emmanuel Macron said President Jair Bolsonaro had lied to him about his stance on climate change.
Tens of thousands of fires have burned across a wide area of the Amazon rainforest this year.
Environmental groups say the fires are linked to Mr Bolsonaro's policies, which he denies.
European leaders have also expressed dismay over the fires. UK Prime Minister Boris Johnson called the fires "not only heartbreaking" but "an international crisis".
"We stand ready to provide whatever help we can to bring them under control and help protect one of Earth's greatest wonders," he added.
German Chancellor Angela Merkel has called the fire an "acute emergency... shocking and threatening not only for Brazil and the other affected countries, but also for the whole world".
Mr Bolsonaro said on Friday that he was considering options for fighting the fires, including deploying the military.
However, he has also accused Mr Macron of meddling for "political gain", and previously said calls to discuss the fires at this weekend's G7 summit in Biarritz, France - which Brazil is not participating in - showed "a misplaced colonialist mindset".
How significant is the trade deal?
Very - the EU-Mercosur trade deal has been described as the EU's biggest deal to date.
It took 20 years of negotiations to strike the agreement with the South American bloc, consisting of Argentina, Brazil, Uruguay and Paraguay.
The EU is Mercosur's second biggest partner in trade in goods, accounting for 20.1% of the total in 2018.
By contrast, EU exports to Mercosur accounted for 2.3% of the EU's total exports in 2018.
The trade includes food and beverages, tobacco and farm products from the South American side and machinery, chemicals and pharmaceutical products from the EU.
On Friday, Mr Bolsonaro appeared to strike a defiant tone, saying on Twitter that Mercosur had reached a trade deal with Efta - a European free trade group of Switzerland, Norway, Iceland and Liechtenstein.
Will international pressure work?
Analysis by Daniel Gallas, BBC News, São Paulo
Mr Bolsonaro is often called the "Trump of the Tropics" because of his unpredictable and brash manners. So it is anyone's guess whether he will back down or carry on with this stance.
Back in June, he hailed the Mercosur-EU trade deal as "historic" and "one of the most important trade deals of all time".
Now his own words and actions are threatening the deal - which still needs to be approved by parliaments of all Mercosur and EU countries.
The deal explicitly says countries have to commit to tackling climate change.
Mr Bolsonaro's son - who wants to become Brazil's ambassador in Washington - retweeted a video calling Mr Macron an idiot.
But even Mr Bolsonaro's agriculture minister and the country's farmers associations have suggested there needs to be a change of tone from the president.
Meanwhile, Finland's finance minister has called on the EU to consider banning Brazilian beef imports.
Finland is currently president of the Council of the EU - a role which is rotated among member states every six months.
Environmental groups have called for protests in cities across Brazil on Friday to demand action to combat the fires.
Hundreds of protesters also gathered outside the Brazilian embassies around the world, including in London, Berlin, Mumbai and Paris.
"We can't stand around waiting for the sky to turn black all the way here in London too," protester Laura Villares House, 33, told BBC Brasil.
Why does the Amazon matter?
The largest rainforest in the world, the Amazon is a vital carbon store that slows down the pace of global warming.
It is known as the "lungs of the world" and is home to about three million species of plants and animals, and one million indigenous people.
UN Secretary-General Antonio Guterres tweeted on Thursday: "In the midst of the global climate crisis, we cannot afford more damage to a major source of oxygen and biodiversity. The Amazon must be protected."
How bad are the fires and who is responsible for them?
Satellite data published by the National Institute for Space Research (Inpe) has shown an increase of 85% this year in fires across Brazil, most of them in the Amazon region. This is the highest number of fires since 2010, though some way off the record in 2005.
Mr Bolsonaro has brushed off the latest data, arguing that it was the season of the "queimada", when farmers burn land to clear it before planting.
However, Inpe has noted that the number of fires is not in line with those normally reported during the dry season.
Wildfires often occur in the dry season in Brazil but they are also deliberately started in efforts to illegally deforest land for cattle ranching.
Conservationists say Mr Bolsonaro has encouraged loggers and farmers to clear the land.
During his campaign, he pledged to limit fines for damaging the rainforest and to weaken the influence of the environmental agency.
Mr Bolsonaro has suggested that non-governmental organisations (NGOs) started the fires, but admitted he had no evidence for this claim. In comments on Thursday, he acknowledged that farmers might be involved in setting fires in the region, according to Reuters news agency.
US space agency Nasa, meanwhile, has said that overall fire activity across the Amazon basin this year has been close to the average compared to the past 15 years.
This article initially stated there was a record number of fires in Brazil this year. After more satellite data was made accessible, it has been updated to reflect the fact the fires are instead the worst since 2010.