With the Obama administration hoping that immigration reform could be passed this year, 17 percent of Americans surveyed back allowing illegal immigrants to become permanent legal residents, according to the poll by the nonpartisan Public Religion Research Institute and the center-left Brookings Institution.
Support for a route to citizenship for the roughly 11 million undocumented U.S. residents is nearly the same as the 63 percent shown in a March 2013 poll, the survey said.
"Even amidst inaction by Congress, support for a path to citizenship for immigrants living in the country illegally remains remarkably broad," Robert Jones, PRRI's chief executive, said in a statement.
Seventy percent of Democrats, 61 percent of independent voters and 51 percent of Republicans favor a path to citizenship for illegal immigrants.
Thirty percent of Republicans favor identifying and deporting all immigrants living in the United States illegally, compared with 11 percent of Democrats.
Majorities of all religious groups except for white evangelical Protestants support a path to citizenship, the poll showed.
Support falls to 48 percent among white evangelical Protestants, an 8-point drop from March 2013.
Sixty-eight percent of Americans favor allowing immigrants living in the country illegally who were brought to the United States as children to gain legal resident status if they join the military or go to college.
President Barack Obama, a Democrat, has made immigration reform a priority. A bill that passed the Democrat-controlled Senate has been stalled in the Republican-controlled House of Representatives.
The telephone survey of 1,538 adults was conducted between April 7 and 27. The margin of error is 3.3 percentage points.