ORLANDO, Fla. — Escalating a confrontation with Senator Marco Rubio of Florida over immigration policy, Senator Ted Cruz of Texas, one of his rivals for the Republican presidential nomination, introduced proposals on Friday outlining his own approach, calling for a halt to increases in legal immigration “so long as American unemployment remains unacceptably high.”

Mr. Cruz did not detail any plans to handle the cases of the roughly 11 million people in the country illegally. But he heightened an attack on Mr. Rubio’s past efforts to forge a bill in the Senate to overhaul the immigration system, repeatedly assailing those who support “amnesty” for undocumented immigrants by suggesting, among other things, that the approach would help Democrats at the ballot box.

“If you’re supporting amnesty, you’re supporting the Obama-Clinton weakness and appeasement to radical Islamic terrorism,” Mr. Cruz told an often raucous crowd at a large church rally here. “If you are supporting amnesty, you’re supporting the Ayatollah Khamenei having nuclear weapons in Iran.”