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Mr. Jindal, meanwhile, was the first Indian-American governor to be elected in any state.

He has supported a federal marriage amendment and won kudos from conservatives for the way he has fought to increase school choice and to overhaul Louisiana’s tax code.

After the 2012 election, Mr. Jindal criticized Mr. Romney’s infamous “47 percent” remark, and said the GOP needs to stop being the “stupid” party.

“What I meant by that was we’ve got to present thoughtful policy solutions to the American people — not just bumper stickers, not just 30-second solutions,” Mr. Jindal said Friday. “We have to have the confidence and the courage in our convictions and show them that our ideas will benefit them.”

Steven Duprey, a Republican National Committee member from New Hampshire who ran Sen. John McCain’s 2008 presidential campaign in the state, said that Mr. Jindal’s appearance in the Granite State is a smart move.

“For candidates who might not have as much money as some others, or who aren’t yet nationally known, this is a great time to come to New Hampshire to start to introduce themselves and to listen to what New Hampshire voters are concerned about,” Mr. Duprey said. “Anyone who thinks the Republican rules only favor the better-known and better-funded candidates should not complain. Instead they should come to New Hampshire, Iowa, South Carolina and Nevada. There are lots of low fares to each of those states.”