STRASBOURG, France (Reuters) - Europe should push for tighter laws to curb the illegal timber trade by making both importers and exporters get licenses to show their wood does not come from endangered rainforests, lawmakers said on Wednesday.

EU countries are an important market for both legally and illegally harvested timber -- the largest importers of plywood and sawnwood from Africa, the second largest from Asia, and a key market for Russia. Much of that wood is suspect.

The European Commission, the EU's executive arm, wants to make licenses obligatory only for exporters, with other measures to reduce the risk of illegally sourced timber entering EU markets. Green groups, and MEPs, say that doesn't go far enough.

"The Amazon-sized hole in the Commission's proposal is that it does not actually prohibit the import and sale of illegally logged timber," said Green MEP Caroline Lucas, whose legal report was backed by the full European Parliament on Wednesday.

Lucas, calling the Commission's timber proposal "vitally important but distressingly weak," said all market operators should be responsible for trading only legally sourced wood.

That report will go before a June meeting of EU farm ministers in Luxembourg, where the issue will be thrashed out.

Debate on a European timber law began more than five years ago and restrictions are currently limited to the terms of voluntary partnerships the European Union has signed with exporters like Ghana. Very few countries have signed up.

Environmental groups say Europe buys 1.2 billion euros ($1.55 billion) worth of illegally felled timber a year, some 20 percent of its imports, and the trade can lead to more forest degradation, fires and poaching.

The WWF estimated last year that nearly a fifth of the wood imported into the European Union is felled illegally or comes from suspect sources, mostly in Russia, Indonesia and China.

"As a major producer and importer of timber, the EU has a key role to play for preservation of forests worldwide," Anke Schulmeister, WWF Forests Policy Officer, said in a statement.

"It is only fair that companies are requested to install systems proving that the timber they sell is legal, respects the environment and the rights of local people," the statement said.

(Reporting by Jeremy Smith, editing by Tim Pearce)