DALLAS — Several members of the House Freedom Caucus advised their state-level counterparts to stop seeking funding from the federal government.

Republican Reps. Andy Biggs of Arizona, Mary Miller of Illinois, Chip Roy of Texas and Ralph Norman of South Carolina attended the first annual State Freedom Caucus Network summit in downtown Dallas this weekend and networked with lawmakers from 12 state legislatures.

“Fight back, push back, pass contrary laws, make a large statement about [federal government spending]. By the way, also start figuring out how to get off of the federal dollars,” Mr. Roy said. “Stop coming to us begging for money, and change the game.”

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Mr. Norman said that state-level Freedom Caucus members must “analyze the cost of taking federal dollars.”

State-level legislators “watch us and they just duplicate a lot of what we’re doing. We didn’t win everything, but we have shifted things more to the right, not just with the speaker, but with the amendments that are now on the floor we’re debating,” Mr. Norman said. “It’s been a good thing.”

Mr. Biggs, who previously served in the Arizona Legislature, said he learned that most state lawmakers’ time is spent responding to federal mandates.

“Many of those mandates were relics from initial grant money, money given to [the state government] from the feds. That’s the hook and then the program dries up. But now get every time you create a program, you create a constituency,” he said, adding that he “begged” every governor he served under to stop taking federal money.

“So we say, ‘Well, we’re going to end the program.’ Well, you can’t end the program, because you now have 30,000 people in Arizona say, ‘Hey, we want that program.’ And so it responds to that,” Mr. Biggs said.

“What I think the state freedom caucuses can do is they can fight those relics, and they can say, when the money dries up, ‘we can’t fund that anymore’ or ‘we’re going to wean it off. We’re going to do something to take that trajectory,’” he said.

Republicans in the Illinois Legislature are in the minority, so the Illinois Freedom Caucus does more messaging tactics to assert political pressure, Ms. Miller said.

She suggested that blue states with lots of farmland like hers oppose the use of solar panels on such property.

“I have a bill — and I know the blue states could do this — is to make it illegal for solar panels to cover Class A and Class B farm ground,” Ms. Miller said. “Because solar panels, when they first sold, was going to be in the desert. [Now] Here we are covering the best farm ground in the world.”

The summit, which the State Freedom Caucus Foundation hosts, kicked off Friday with more than 200 lawmakers from around the U.S., members of third-party conservative organizations. State lawmakers attended political education seminars with speakers and capped the weekend Saturday night with an awards gala.