Sen. Ted Cruz, a leading voice in the national debate over immigration, on Monday appeared before a group that supports curbing both illegal and legal immigration and urged his fellow Republicans in the House to reject immigration reforms approved earlier by the Senate.

Cruz, the son of a legal immigrant from Cuba, has not publicly called for limits on legal immigration and made he no mention of such restrictions in his address to the DC March for Jobs outside the Capitol. But March organizers — including the Black American Leadership Alliance and Tea Party groups — do support curbing legal immigration, saying it could take jobs away from “millions of American citizens.” Cruz also claimed the Senate immigration reform would cost Americans’ jobs but without specific reference to legal immigrants.