WASHINGTON — At a Hyatt hotel blocks from Capitol Hill, Republican state lawmakers are gathering for a meeting of the American Legislative Exchange Council to determine how to use the new power they’ll wield outside of Washington.

They were exhorted to call a constitutional convention to roll back Washington’s reach. An Illinois lawmaker said he saw a chance to weaken the Environmental Protection Agency. A Republican in New Mexico, where the party is taking command of the state House for the first time since the 1950s, said she would like to curb union power.

“There are a lot of things to do and this is our opportunity,” New Mexico State Rep. Yvette Herrell said. “We need to create opportunities in terms of jobs.”

Last month Republicans expanded their control of governorships to 31 and picked up seven legislative chambers for a record 69.

With power divided at the federal level, state Republicans have used their sway to cut taxes, restrict access to abortions and roll back powers of organized labor, a pillar of the Democratic Party.

The American Legislative Exchange Council is a corporate-funded nonprofit that designs business-friendly legislation for the state level. About one-fourth of state legislators belong; of those, 80 percent are Republican.

Following the Florida shooting death of Trayvon Martin in 2012, ALEC was criticized for its role in advancing so-called Stand Your Ground self-defense laws. Companies including Google and Yahoo this year dropped out of the group, which has worked against state renewable energy laws intended to address climate change.

The four-day meeting, which began Tuesday, includes seminars on overhauling public-employee pensions, tax policy and giving residents more power to choose schools, as well as closed-door sessions to discuss prospective model legislation. Tobacco giant Altria Group, United Parcel Service Inc. and Peabody Energy Corp., the largest U.S. coal producer by sales, are among its sponsors.

More local government control is a major theme of the conference.