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Those courses of action outlined in the bills “are not options we have embraced but are at least legitimate,” said Ilir Zherka, director of pro-home-rule group D.C. Vote.

Mr. Zherka said his group was disappointed with Mr. Gohmert’s gun measure because he appeared to be a “convert” when he introduced his bills in 2009.

“It’s a curious thing,” he said. “It really sounds like he’s trying to have it both ways.”

If GOP leaders and tea party members are proponents of local ruleand states’ rights, he added, then interfering with the District “would not be keeping with these principles.”

Republican members of Congress, including Mr. Gohmert, couched the potential change to D.C. laws as a way to ensure consistent application of the constitutional right to carry firearms.

“I’m a big states’ rights guy,” Mr. Gowdy said. “But the states’ rights come in where the Constitution has not already spoken. It’s already spoken with respect to the Second Amendment.”

Still, the firestorm continues between proponents of statehood and those who view the District as an enclave controlled by Congress.

Mr. Gohmert rejects the idea of making the District the 51st state, even if a boundary is drawn around the sector of federal buildings.

“Does that mean every 600,000-person area should be a state because they don’t want to be part of an area, they want to be autonomous?” Mr. Gohmert asked. “I know parts of east Texas that want to be their own state.”