By Edith Honan

NEW YORK, April 30 (Reuters) - The executive director of the gun control group founded by former New York Mayor Michael Bloomberg, which has emerged as a leading counterweight to the National Rifle Association, said on Wednesday he would step down from the organization in June.

Mark Glaze was named head of Mayors Against Illegal Guns in 2011, three weeks after a gunman opened fire in an Arizona shopping plaza, killing six people and critically wounding Congresswoman Gabrielle Giffords. It was the first in a string of mass shootings, including one at a Newtown, Connecticut, elementary school in 2012, that helped galvanize the gun control movement.

Glaze helped turn the group into the largest and most prominent gun safety organization in America.

Last year, he helped orchestrate MAIG's merger with another group, Moms Demand Action For Gun Sense in America, and launch a new umbrella group, Everytown for Gun Safety, earlier this month.

"It is time for me to hand off the fight to somebody else," Glaze, 43, said in an interview. "The issue is unbelievably important to me. But it's a tough issue and a tough grind. And there's a point where you feel you've done all you can do."

Glaze said he planned to do some consulting.

"I think I've learned a lot about how to run a simultaneous national and state issue campaign on very difficult issues against very tough opponents. And I think there are other organizations who are fighting similar fights who could use the help," he said.

Even as the movement has grown, it has suffered stinging losses and the NRA remains a potent rival. After the Newtown shooting, a bill to expand the use of background checks, which was backed by President Barack Obama and championed by MAIG, failed to win passage in Congress.

"The fight for better gun control has worn out many a warrior," said Adam Winkler, a law professor and the author of the book "Gunfight."

Glaze, whose father was a licensed gun dealer in Colorado, previously worked at the Washington-based Raben Group. He joined MAIG several years before taking over as executive director.

He voiced optimism about the gun control movement and pushed aside criticism it had fallen short.

"People who thought that you were going to win the hardest public policy fight there is overnight and defeat the toughest special interest were kidding themselves," he said. (Reporting by Edith Honan; Editing by Leslie Adler)