International fury at the EU law led Climate Commissioner Connie Hedegaard last year to propose a temporary exemption for intercontinental flights.
The European Parliament's Environment Committee voted in favour of her proposal, dubbed "Stop the Clock". The move needs the endorsement of a full parliamentary session in April, but has so much support that it is unlikely to be overturned.
The committee strengthened the wording to underline the fact that the suspension could be prolonged beyond a year only if "clear and sufficient" progress were made at the International Civil Aviation Organization (ICAO), the UN body seeking an alternative plan to curbing airline emissions.
"There's no excuse any more. Nobody can say now that the EU is obstructing any agreement," said German Christian Democrat Peter Liese.
"I appeal especially to US President Obama, who has been awarded the Nobel Peace Prize among other things for his commitment to tackle climate change, and to Secretary of State [John] Kerry," he added. "They could lose all the credibility if they continue opposing a solution in this important area."
So far, campaign groups say Washington's position paper ahead of the next ICAO-sponsored talks in March shows it is proposing a measure that would cover only a small part of airline emissions.
The International Air Transport Association said the EU law had been an obstacle to a global deal.
"With that roadblock removed, we are well positioned for a breakthrough on market-based measures," said Tony Tyler, IATA's director general.
But he said "the devil will be in the details" and it was crucial to have an agreement that preserved "fair competition".
The EU Emissions Trading System (ETS) continues to apply to flights between EU airports, which some airlines maintain is an unfair cost burden, given the intercontinental freeze.
The Commission argues that the cost is in fact minimal - only about €2 per passenger per long-haul flight given the current price of carbon permits, which have fallen to a record low of less than €3 per tonne.