Donald Trump said people can immigrate to the U.S., but only if they do so legally.
"If we need people, they have to come into this country legally. It's fine. If they come in they have to come in legally," he said during Wednesday's Republican debate.
Sen. Marco Rubio said the legal immigration system should be scrutinized as well.
"Our legal immigration system from now on has to be merit-based," he said. To be considered, an immigrant must show skills and a willingness to be an American, Rubio added.
Rubio himself is the son of immigrants from Cuba.
In August, Trump said he would increase the prevailing wage for H-1B visa recipients in order to encourage employers to hire native workers for well-paying science, technology, engineering and math jobs, rather than flying in foreign workers.
U.S. Citizenship and Immigration Services grants H-1B visas to a limited number of skilled foreigners who agree to work in specialty fields.
Trump said too many workers are being hired at the program's lowest allowable wage levels at the expense of women and people of color, two notoriously underrepresented groups in Silicon Valley.
— CNBC's Tom DiChristopher contributed to this report.