Do immigrants take jobs from Americans and lower their wages by working for less?

The answer, according to a report published on Wednesday by the National Academies of Sciences, Engineering and Medicine, is no, immigrants do not take American jobs — but with some caveats.

The question is at the heart of the furious debate over immigration that has divided the country and polarized the presidential race. Many American workers, struggling to recover from the recession, have said they feel squeezed out by immigrants.

Donald J. Trump, the Republican nominee, has called for a crackdown on illegal immigrants, saying they “compete directly against vulnerable American workers.” He promises to cut back legal immigration with new controls he says would “boost wages and ensure open jobs are offered to American workers first.”

Hillary Clinton, his Democratic rival, takes an upbeat view, saying immigrants contribute to the economy whether they are here legally or not, by providing labor for American employers and opening businesses that create jobs for Americans rather than taking them.