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 might attend.

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,” Mr. Curtis said in an interview. “It’s terrible that Republicans can’t even go talk about it without being embarrassed.”

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 Trump adviser 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 avoid discussing climate change, he said.

In Utah, where the furtive February 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 held what was billed as the first rally for “conservative” climate action. They carried signs that read “This Is What an Environmentalist Looks Like.”

On Capitol Hill, Kevin McCarthy, the House Republican leader, plans to start a Republican task force on climate change, his staff confirmed.

And on Wednesday Mr. Curtis plans to announce 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.” So far 38 Republican House members have joined, his staff said.