A small but growing number of Republicans say the G.O.P. needs a coherent climate strategy and formed a “Conservative Climate Caucus” on Capitol Hill.

When Representative John Curtis quietly approached fellow Republicans to invite them to discuss climate change at a clandestine meeting in his home state of Utah, he hoped a half dozen members might attend.

Soon the guest list blew past expectations as lawmakers heard about the gathering and asked to be included. For two days in February, 24 Republicans gathered in a ballroom of the Grand America Hotel in Salt Lake City where they brainstormed ways to get their party to engage on a planetary problem it has ignored for decades.

“Some came with the promise of being anonymous. It’s terrible that Republicans can’t even go talk about it without being embarrassed,” Mr. Curtis said in an interview.

For four years under President Donald J. Trump, even uttering the phrase “climate change” was verboten for many Republicans. His administration scrubbed the words from federal websites, tried to censor testimony to Congress and mocked the science linking rising fossil fuel emissions to a warming planet.

Now, many in the Republican Party are coming to terms with what polls have been saying for years: independents, suburban voters and especially young Republicans are worried about climate change and want the government to take action.

“There is a recognition within the G.O.P. that if the party is going to be competitive in national elections, in purple states and purple districts, there needs to be some type of credible position on climate change,” said George David Banks, a former adviser to President Trump and now a senior fellow at the nonprofit Bipartisan Policy Center, a centrist Washington think tank. Republicans realize it is now “a political liability” to dismiss or even avoid discussing climate change, he said.In Utah, where the furtive climate meeting occurred, a group of state Republican lawmakers this month called for polluters to pay a price for emitting carbon dioxide, the main heat-trapping gas.

The same week in Miami, a group of young Republicans carrying signs that read “This Is What an Environmentalist Looks Like,” held what was billed as the first rally for “conservative” climate action.

On Capitol Hill, Kevin McCarthy, the House Republican leader, plans to start a Republican task force on climate change, his staff confirmed. Mr. McCarthy declined a request for an interview.

And on Wednesday Mr. Curtis announced the formation of the Conservative Climate Caucus, aimed at educating his party about global warming and developing policies to counter what the caucus terms “radical progressive climate proposals.” As of Tuesday morning, 52 Republican House members have joined, his staff said.

“It’s my hope that any Republican that belongs to this caucus, if asked about climate in a town-hall meeting, will feel very comfortable talking about it,” Mr. Curtis said, adding, “I fear that too often Republicans have simply said what they don’t like without adding on ‘but here’s our ideas.’”

Those ideas include limited government, free-market policies to curb greenhouse gas emissions, as formulated by new conservative think tanks. One is C3 Solutions, which is co-led by a former aide to the late Senator Tom Coburn of Oklahoma, who called global warming “crap.” The organization also recently attracted an energy policy expert from the Heritage Foundation, a conservative group that until recently promoted vociferous critics of climate change.

A package of bills Mr. McCarthy introduced on Earth Day championed carbon capture, a nascent and expensive technology that catches carbon emissions generated by power plants or factories and stores them before they escape into the atmosphere. It also promoted tree planting and expansion of nuclear energy, a carbon-free power source that many Republicans prefer over wind or solar energy.