Despite Donald Trump's campaign promise to crack down on illegal immigration, a majority of Americans would like to see undocumented immigrants stay in the country and get a chance to become citizens, according to a new poll from Quinnipiac University.

The response, 60 percent, was the highest since the Quinnipiac poll started asking the question four years ago.

"Though it drew cheers on the campaign trail, the fiery rhetoric about redirecting the path to citizenship in the U.S. back to the Mexican border is actually losing support," Tim Malloy, the poll's assistant director, said in a statement.

Trump has vowed to deport millions of immigrants in the United States illegally, focusing on those with criminal records, and strengthen border security. He has also met with potential Cabinet picks who have espoused anti-immigrant policies, most notably Kansas Secretary of State Kris Kobach, who warned last week that no undocumented immigrants would get a "free pass."

Related: Trump Transition Team Filled with Hardline Anti-Immigration Advocates

But Trump himself hasn't said much since the election about his plans for broader immigration policy. In an interview with the New York Times this week, Trump said he wanted to pass an immigration law "that's fair."

Immigration doesn't appear to be all that important to Americans, according to the poll, which was conducted Nov. 17-20 among 1,071 respondents. The results have a margin of error of 3 percentage points.

Asked what Trump's top priority should be when he takes office in January, only 6 percent of respondents said immigration. The top issue was the economy, with 24 percent naming it as the most important.

Another majority, 55 percent, said they opposed building a wall along the Mexican border, one of Trumps's signature pledges. Forty-two percent said they wanted a wall.

But 50 percent said they supported suspending immigration from "terror prone" regions, even if that meant turning away refugees. Forty-four percent said they opposed doing that.

On the question of what to do with undocumented immigrants living in the United States, the divide was deeper. Sixty percent said they were in favor of allowing them to stay and to eventually apply for citizenship; 12 percent said they should be allowed to stay but not be allowed to apply for citizenship; and 25 percent said undocumented immigrants should be forced to leave.

Across the board, partisan differences were even wider, with Democrats holding a much more lenient view toward immigrants than Republicans.