Last week, arbitrators from the WTO granted President Donald Trump's administration the right to levy billions against imports of European goods for what they say are illegal subsidies granted to planemaker Airbus by the European governments of Germany, France, Spain, and the United Kingdom.
Trump subsequently described the ruling as a "nice victory."
The EU has its own separate case before the WTO, in which it argues that the U.S. planemaker Boeing receives unfair financial assistance from the U.S. federal government.
The EU has said it wants to agree on a way forward with Washington by imposing a new regime on aircraft subsidies.
Director general of the WTO, Roberto Azevedo, told CNBC’s Joumanna Bercetche in Geneva Thursday that he hoped both sides would agree to conduct talks.
"I hope parties will sit down and talk and find a negotiated solution because the last thing we need at this point in time is an escalation of tariff barriers and trade restrictions," said Azevedo.
The WTO boss said slapping tariffs on imports tended to generate a "domino effect" of barriers to trade.
"You cannot expect that you can impose tariffs and barriers and everyone else is going to sit down and applaud quietly. They are going to respond," he said.
Britain and Northern Ireland are now just three weeks from the next deadline (Oct. 31) which the U.K. government insists will see the U.K. leave the European Union.
No deal has been agreed, either in the U.K Parliament or between London and Brussels.
Azevedo told CNBC that after a no-deal exit the U.K. can immediately default to trading under WTO rules. He warned however that any attempt to invoke an obscure trade law — Article 24 of the General Agreement on Tariffs and Trade (Gatt) — to allow continued free trade would fail.
"What Article 24 says is if you do have an agreement you will have time to implement that agreement. But if there is no agreement then Article 24 would not apply, by definition," said the WTO chief.
Azevedo said a "non-negotiated" Brexit would hurt both EU and U.K. growth.
"It would not stop but there would be consequences. More barriers, more tariffs, and those things impact negatively on the economy," he said.