(Adds conservative group's opposition, lawmaker quotes)

By David Lawder

WASHINGTON, May 21 (Reuters) - The U.S. Export-Import Bank moved a step closer to avoiding closure on Thursday as Senate Republican Leader Mitch McConnell agreed to hold a vote on renewing its charter in June.

The decision gives Congress a legislative vehicle to start considering the fate of the federal export credit lender, with conservative House of Representatives Republicans bent on closing it down. Its charter is set to expire on June 30.

Ex-Im provides loans and insurance to help foreign customers buy goods from U.S. manufacturers. Conservative lawmakers and political groups have said Ex-Im fosters "crony capitalism" and puts U.S. taxpayers at risk.

Large corporations including Boeing and General Electric have warned that closing the bank would mean the loss of major sales contracts to overseas rivals that have aggressive lending support from their own governments, which in turn, would cost American jobs.

McConnell agreed to hold the Ex-Im vote next month to help secure Democratic support for separate legislation giving President Barack Obama "fast track" negotiating authority for a major Pacific Rim trade deal. After his pledge, the trade bill cleared a major procedural hurdle on Thursday

Republican House of Representatives Speaker John Boehner said that, if the Senate passes a bill to reauthorize Ex-Im, he will take it up in the House under an "open amendment" process.

House Financial Services Chairman Jeb Hensarling, a major Ex-Im opponent, has made no move to consider Ex-Im legislation and has said he is prepared to let it simply expire.

Differences among House Republicans over Ex-Im were exposed when the chairman of a 170-member House conservative caucus on Thursday pledged the group was opposed to the bank.

"Federal bureaucrats should not be picking business winners and losers," Republican Study Committee Chairman Bill Flores said in a statement.

But some members of the group immediately distanced themselves from Flores' position. Republican Representative Steven Fincher said 33 RSC members are co-sponsors of his stalled legislation to reauthorize the bank.

"These members realize the importance of the bank and realize that our constituents do not send us to Washington to shut the world down," Fincher said. "It's unacceptable for Congress to stand idly by and let millions of jobs dissolve." (Reporting By David Lawder and Anna Yukhananov; Editing by Kevin Drawbaugh, Susan Heavey, Emily Stephenson and Leslie Adler)