Barack Obama has signed a law excluding US airlines from the European Union's carbon trading scheme, delivering a blow to campaigners' hopes for stronger climate action during the president's second term.

Environmental campaigners had urged Obama to veto the aviation bill as a sign of his commitment to fighting climate change in his second term.

The White House said in a statement Obama still saw climate change as a priority but that he disagreed with subjecting US and other foreign airlines to the EU emissions trading scheme.

"The Obama administration is firmly committed to reducing harmful carbon pollution from civil aviation both domestically and internationally," a White House statement to reporters said. But "the application of the EU ETS to non-EU air carriers is the wrong way to achieve that objective".

The White House said the Obama administration would work to resolve airline emissions through the International Civil Aviation Organisation.

But the move was disappointing to European officials and to campaigners in the US who had urged Obama to veto the bill.

After winning re-election Obama listed climate change as one of the three main challenges facing the country. Campaigners had hoped he would make the fight against climate change part of his legacy.

The World Wildlife Fund said it was disappointed the bill had passed. "However, there is a silver lining here – the administration has appointed high-level representatives to pursue a global solution for aviation and climate," WWF said.

Connie Hedegaard, the EU's climate commissioner, tweeted: "Aviation ETS: So far the re-elected Pres. #Obama #climate policies look EXACTLY as in first term. Wonder when we'll see the announced change?"

The bill signed by Obama on Tuesday was unusual in that it specifically exempted US companies from complying with international law.

But American airlines had pushed hard for the bill, which had support from Democrats as well as Republicans in Congress.

Commercial carriers argued the EU's carbon tax was unfair because it would require airlines to pay for emissions on the entire transatlantic flight, not just through European air space. The main airline lobby group said it would cost the industry $3.1bn by 2020.

"It never made a bit of sense for European governments to tax our citizens for flying over our own airspace," said Claire McCaskill, the Democratic senator from Missouri.

Under the original plan airlines would have had to begin paying for the carbon emitted during flights early next year. Carriers were to reduce their emissions 3% from 2006 levels next year and 5% by 2020.

But the EU put the programme on hold for a year for non-European carriers to allow time for a global agreement on aviation emissions.