Green parties have swept to their strongest ever showing in European elections, boosting their tally of MEPs to a projected 71 compared with 52 last time. The result gives them every chance of becoming kingmakers in a newly fragmented parliament.

“Thank you so much for your trust in us Greens,” a delighted Ska Keller, one of the European Greens’ two lead candidates for the post of European commission president, told a press conference in Brussels.

“This is a mandate for real change: for climate protection, a social Europe, more democracy and stronger rule of law.” Above all, Keller said, the Greens “want to achieve climate action now – because if we wait any longer, it will be a disaster”.

Any parliamentary group that wanted Green support would have to “deliver on our three key principles: climate action, civil liberties and social justice”, she said. “For us it’s clear: this is all about content.”

With the European parliament’s main centre-right and centre-left groups both losing seats and their historic joint majority, and populist Eurosceptic parties returning in larger numbers than before, Green MEPs’ votes could well prove critical to a broad pro-EU alliance in the 751-seat assembly.

The Greens’ surge was strongest in Germany, where Die Grünen finished second behind Angela Merkel’s centre-right CDU with almost 21% of the vote, according to provisional estimates – nearly double their 2014 total.

Finland’s Greens also came second with 16% of the vote, while in a major upset, Europe Écologie-Les Verts, led by a former senior Greenpeace figure, came third in France with 13.3%, up from 8.9%. Against all expectations, a Portuguese Green party won its first European parliamentary seat.

Ireland’s Green party trebled its previous score to 15% from 5%, meaning it will be sending MEPs to the Strasbourg parliament for the first time in 20 years, while in the Netherlands, GreenLeft improved to garner nearly 10.5% of the vote.

“We will fight hard for everything in our manifesto,” promised the party’s other main candidate for the EU’s top job, the Dutch MEP Bas Eickhout. “We are going to be genuinely tough on climate action.”

Greens in Denmark, Sweden, Belgium, Luxembourg and Austria also scored highly, building on recent election successes as progressive voters, mainly in northern Europe, are increasingly drawn to their pro-EU stance, humane approach to migration and strong positions on existential issues such as the climate crisis and sustainability.

Greens are in government in Sweden and Luxembourg; have 20 MPs in Finland after scoring 11.5% in April’s general election; look set to join a centre-left coalition after elections in Denmark next month; are strong contenders in Belgium’s general election; have run Amsterdam city council since last March; and currently co-rule nine of Germany’s 16 states.

At the EU level, more than 30 national parties make up the European Green party. They are part of the Greens/EFA group in the European parliament with progressive regionalist parties such as the Scottish National party (SNP), Wales’ Plaid Cymru and the Swedish and German Pirate parties.

In exchange for their support, they will exert maximum pressure on climate policy, Eickhout said in a pre-election interview, but will also push for more social justice when it comes to who winds up footing the bill for the green transition.

The party will further demand a radical change of tack on rule of law from the centre-right European People’s party (EPP) group, which has come under heavy fire for its lukewarm criticism of the Hungarian prime minister, Viktor Orbán.

“We have to decide: are we a Europe that will defend democratic values, or just a collection of strong national states?” Eickhout said, adding that he saw three main factors behind the Green movement’s improving fortunes.

Concern about climate change has “rocketed up people’s priorities,” he said; Green parties had shown themselves “more than capable” in national and local government; and they were also benefiting from progressives’ declining support for centre-left parties which backed austerity after the 2008 financial crisis.

• This article was amended on 27 May 2019. An earlier version misnamed the Scottish National party as the “Scottish Nationalist party”.