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Young Republicans are much more likely to have favorable views of immigration and to support a path to citizenship for immigrants in the United States illegally than are older Republican voters, according to a survey published on Tuesday by the Public Religion Research Institute, a nonpartisan research group. The divide could mean trouble in the general election for either of the two leading Republican candidates, Donald J. Trump and Senator Ted Cruz of Texas, who have called for mass deportation of 11 million undocumented immigrants.

In the survey, 63 percent of Republicans under 30 said they supported giving those immigrants a chance to become citizens if they met certain requirements. Only 20 percent of young Republicans said they would identify and deport them. By contrast, about a third — 34 percent — of Republicans 65 and over favored deportation, and fewer than half — 47 percent — said they supported a pathway to citizenship for those immigrants.

A third option, allowing the immigrants to become permanent legal residents but not citizens, was not supported by more than 15 percent of either group.

The institute’s survey is unusual because of the size and duration of its sample. The report is based on 42,586 telephone interviews conducted in English and Spanish from April 29, 2015, to Jan. 7, 2016. The margin of error is plus or minus one point.

Mr. Trump’s pledges to expel illegal immigrants and to build a wall along the border with Mexico consistently draw cheers at his rallies. Mr. Cruz has followed Mr. Trump and hardened his position, saying he would deport illegal immigrants and would not allow them to return.

In general, Republicans’ views of foreign newcomers are negative, the survey suggests, with 53 percent saying that recent immigration “threatens traditional American customs and values,” while only about a third — 32 percent — say immigrants “strengthen American society.” Among conservative Republicans, 58 percent think immigration is bad for the country.

But 51 percent of young Republicans say immigrants make the country stronger.

Over all, three in 10 Republicans favor deporting illegal immigrants. According to the survey, those voters are older, white and working class, with a high school education or less; they say they are conservative, and many are evangelical Christians. In short, they are the voters who have flocked to support Mr. Trump in the Republican race, and who, in smaller numbers, have also backed Mr. Cruz.

But even after months of the candidates’ scorching comments, a slim majority — 52 percent — of all Republicans say they would offer a path to citizenship for immigrants in the United States illegally, a finding that remained “remarkably stable throughout 2015,” according to the report.

“Many younger Republicans have grown up in a much more diverse world,” said Robert P. Jones, the chief executive of the research institute. He said the survey suggested that either Mr. Trump or Mr. Cruz would have to soften their positions to mobilize young Republicans to vote in November.

“A really hard line on immigration has the potential not just to fall flat but to push off younger Republicans,” Mr. Jones said.

Among Democrats, 72 percent back a path to citizenship, while 11 percent support deportation, and 14 percent prefer allowing undocumented immigrants to stay as legal residents without becoming citizens.