"If you wish to live and work in America, then we will find a place for you," Paul said Tuesday in a speech before the U.S. Hispanic Chamber of Commerce in Washington.
"The solution doesn't have to be amnesty or deportation," he said. "A middle ground might be called probation, where those who came illegally become legal through a probationary period."
Paul didn't specify in his speech whether he would endorse letting the 11 million undocumented immigrants already in the U.S. become citizens, in contrast to a bipartisan group of senators who call for a path to citizenship. Paul's speech suggested giving "probationary work visas to immigrants who are willing to work."
Paul, 50, son of former Texas Rep. and Republican presidential candidate Ron Paul, is a leader of the limited-government tea party movement. His decision to back an immigration overhaul may help congressional advocates pressing for a broad rewrite of immigration laws. The Senate group is expecting to unveil its plan next month.
Paul's announcement addresses his own political ambitions and the importance of the immigration issue to the Republican Party, said Brad Blakeman, a Republican strategist and former deputy assistant to President George W. Bush.
"There is no tea party in the political sense, no central leader, no candidates, so Rand Paul is stuck between a rock and a hard place," Blakeman said. "He is coming to the center and adopting policies that a Republican nominee would have to support if you want the nomination, and more importantly, to be electable."
One member of the bipartisan Senate group is Florida Sen. Marco Rubio, another potential 2016 Republican candidate who has been advocating a path to citizenship. He declined to comment on Paul's plan, saying he hadn't seen it.
Paul's position differs from the principles of the bipartisan Senate group. He endorsed a quicker path to legal status instead of citizenship and said a path to citizenship already exists under current law.
Paul proposed no additional obligations for employers, saying, "My plan will not impose a national ID card or mandatory E-Verify, forcing businesses to become policemen."
Like the bipartisan Senate group, Paul proposed allowing work permits and other authorizations only after Congress certifies that U.S. border control has been improved.
House Speaker John Boehner, R-Ohio, on Tuesday avoided questions on whether he supports steps that could lead to citizenship for those who came to the U.S. illegally. Still, the speaker said overhauling the nation's immigration system is a "top priority" in the Republican-led House.
Boehner said he met with four Republican members of a bipartisan House group that has been meeting in secret for about four years to work on an immigration plan. Boehner said the Republican members are "basically in agreement" with the Democrats on how to proceed on legislation.
In his speech, Paul criticized his party's handling of the issue.
"Hispanics should be a natural and sizable part of the Republican base," he said.
Among the first pieces of legislation Paul co-sponsored after arriving in Washington in January 2011 was a bill to amend the Constitution to end birthright U.S. citizenship for children of undocumented immigrants. Citizenship would be granted to those born in the U.S. to a parent who is a citizen, has permanent residency status or serves in the U.S. military.
Hundreds of women immigrants and community leaders rallied Tuesday in Washington push for a new immigration law in an event attended by Democratic Sens. Barbara Boxer of California and Mazie Hirono of Hawaii.
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