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Mr. Rubio, a Cuban-American in his first term whose star is rising rapidly in his party, has outlined views in recent days that set him apart from many other Republican conservatives, who reject any legalization as a form of amnesty that rewards immigrant lawbreakers. Mr. Rubio said he would not rule out some kind of legal status for immigrants in the United States illegally, although he insists that any measures should not penalize immigrants who have tried to come here through legal channels.

Mr. Rubio described his proposals in interviews last week with the Wall Street Journal editorial page and with The New York Times. By Monday he was already gathering support, as Representative Paul D. Ryan of Wisconsin, a conservative who was the Republicans' vice-presidential nominee last year, endorsed Mr. Rubio's ideas.

Mr. Rubio laid out three: aside from fair treatment for foreigners who play by the rules, he said, any legislation should also recognize that legal immigration has been a boon to the United States in the past and is "critical to our future." He would also insist on new measures to ensure strict enforcement at the border and within the country.

"We can't have the kind of vibrant growth we need and the economy we want, based on limited government and free enterprise, if we don't have a legal immigration system that works," Mr. Rubio said. "And in order to have a system that works, we have to deal with those people who are already here illegally."

Mr. Ryan, on his Facebook page, wrote that Mr. Rubio was "exactly right on the need to fix our broken immigration system."

"I support the principles he's outlined," Mr. Ryan said, "modernization of our immigration laws; stronger security to curb illegal immigration; and respect for the rule of law in addressing the complex challenge of the undocumented population."

  As one of three Hispanics in the Senate, Mr. Rubio, who won his seat in 2010 with support from the Tea Party, seemed to be trying to set a new tone for his party to discuss immigration. Many Republican leaders have been reconsidering the party's stance on the issue since the November election, when Latinos, the electorate's fastest-growing group, overwhelmingly supported Mr. Obama.

Strikingly, Mr. Rubio's principles did not sound that different from proposals for an immigration overhaul by Mr. Obama, Democratic leaders and a handful of other Republicans. Aside from work under way at the White House on legislation, a bipartisan group of Senators has been meeting to draft a bill.

Where Mr. Rubio differed significantly with Democrats was on the legal pathway illegal immigrants would follow, with him proposing a long and indirect course before some of those immigrants could apply to become American citizens.

In a telephone interview, Mr. Rubio said a starting point for his plan was recognizing that the current immigration system was "burdensome, bureaucratic, difficult to navigate and sometimes it just doesn't work."

Mr. Rubio said he would seek to reorient the visa system to bring in more educated immigrants with skills in technology and science. As for the estimated 11 million illegal immigrants in the country, Mr. Rubio said, "We have to understand these folks are here to stay." He added that most of them had not committed serious or violent crimes.

"The right way to deal with them is not amnesty," Mr. Rubio said, "and it is not a special pathway to citizenship." Instead, he said, he would offer a provisional legal status to immigrants who passed criminal background checks, paid fines and passed English and civics tests.

But, he said, "ultimately it's not good for our country to have people permanently trapped in that status where they can't become citizens." After a certain period, he said, immigrants would be allowed to apply to become legal permanent residents, a status that would eventually allow them to become citizens.

The current system is clogged with huge backlogs, with some immigrants waiting as long as two decades to receive visas. Mr. Rubio said that potentially large flaws in his plan would be worked out in negotiations.

Although Mr. Rubio said it would be better for Congress to take up the complex issues in separate pieces of legislation, he said he would not insist on that.

Mr. Rubio said he would offer a faster track to citizenship for young undocumented immigrants who came here as children. Members of Mr. Rubio's staff have been meeting with leaders of United We Dream, the largest organization of those young immigrants.

"To me the most surprising thing was that he was talking about a pathway to citizenship," Lorella Praeli, a leader of the organization, said on Monday. "There has been such a shift in the tone, in his vision."

Some conservative Republicans made it clear they would not support Mr. Rubio. In a statement, Senator Jeff Sessions of Alabama said Mr. Obama had undercut the chances for an overhaul by weakening enforcement. "If the administration had spent the last four years ending illegality instead of abetting it," he said, "we would be in a better position for some kind of agreement."