LANSING, Mich. — Michigan moved to the brink of establishing hunting seasons for the gray wolf early today, as the state Legislature gave final approval to a bill designating the once-imperiled species a game animal.

Four decades after the federal government outlawed killing wolves to prevent them from going extinct in the lower 48 states, the resilient predators have bounced back in the Upper Great Lakes and Northern Rockies. Their combined population exceeded 4,000 when dropped from the endangered species list in January.

Since then, hunting has begun in five states — Minnesota, Wisconsin, Idaho, Montana and Wyoming — and officials say more than 640 wolves have been trapped or shot. Environmentalists are fighting in court to restore federal protections in Wyoming, and the Humane Society of the United States has served notice of intent to do likewise in the Great Lakes region.

But with the population in Michigan’s Upper Peninsula around 700, legislators say it’s time to let hunters thin their ranks. Complaints of livestock depredation are on the rise, and legislators say emboldened wolves are edging too close to urban areas. Similar issues led officials to approve hunts this fall in Minnesota, where 261 wolves had been killed as of this week, and Wisconsin, where the latest toll was 107. Both states are approaching kill quotas set by wildlife managers.

“I don’t expect we’ll have a statewide hunt” in Michigan, said state Sen. Tom Casperson, an Escanaba Republican who sponsored the game species bill. “But we need to give wildlife managers a tool to slow down the population in particular areas where it’s exploding.”

The state House approved the measure Wednesday and returned it to the Senate, which had passed it earlier, for consideration of a technical amendment that was approved today. Gov. Rick Snyder is expected to sign the bill, which is supported by the Department of Natural Resources.

Although it authorizes regulated hunting, the decision about whether and when to have seasons rests with the Michigan Natural Resources Commission, whose seven members are appointed by the governor.

J.R. Richardson, the panel’s new chairman, said during a meeting Thursday that it will be guided by a management plan the department put together with advice from groups representing interests such as hunting, animal welfare and environmental protection, and farming.

He requested an update on the wolf’s status in January and promised to continue consulting with the public, including Indian tribal governments, which fought the game species bills and contend there isn’t enough scientific evidence to justify hunts. Wolves have a cherished status in many tribes’ spiritual traditions.

“If a bill delegating authority to create a hunt is signed into law, it will be up to the commission to lay out a socially responsible framework for population management on a limited basis to help resolve conflicts in specific areas,” said Richardson, a resident of Ontonagon in the Upper Peninsula.

The Humane Society of the United States urged Snyder to veto the bill, saying Michigan’s wolves are “just starting to recover.”

“It’s not right to spend decades protecting wolves from extinction only to turn around and allow them to be killed for sport,” state director Jill Fritz said.