WASHINGTON, June 16 (Reuters) - Republican Senator Marco Rubio said on Sunday he still supports a bill to overhaul the U.S. immigration, but reiterated that he wants its stipulations on border security to be tightened in order for the legislation to win approval from Congress.
Rubio, one of the so-called Gang of Eight Republican and Democratic senators steering the bill, has been criticized by Conservative Republicans as being too soft and there have been concerns he could walk way from the legislation.
The lawmaker from Florida said on ABC's "This Week" program that the bill was about 96 percent ready but should include strong measures on border security to ensure there would not be another wave of illegal immigration in the future.
"If we do that, this bill will have strong bipartisan support," Rubio said.
Rubio said he did not believe the Senate would try to push the legislation through without toughening the language on border security.
"If we fail, we're going to keep trying, because at the end of the day, the only way we're going to pass an immigration reform law out of the House and Senate so the president can sign it is, that it has real border security measures within it."
Rubio declined to engage in "hypotheticals and ultimatums" about whether or not he could vote for the bill without added border security provisions. He played down accusations from conservative critics that he has been influenced by Democratic lawmakers in the reform debate.
The bill currently being debated in the U.S. Senate was rolled out in April and would provide a 13-year path to citizenship for 11 million illegal immigrants.
Rubio's Democratic counterpart Robert Menendez cautioned Republicans against trying to use the border security issue to delay the passage of the legislation.
"We are open to constructive elements of how border security can be further achieved, but not if at the end of the day you're just simply using that as an excuse not to permit a pathway to legalization," said Menendez on CNN's State of the Union program.
Republicans and Democrats are anxious to tackle immigration reform, after the increasingly influential Latino vote turned out heavily in favor of President Barack Obama and his Democrats in the November 2012 election.
This has not been lost on some Republicans, including South Carolina Senator Lindsey Graham, who said the immigration bill would decide who wins the White House in 2016.
"If we don't pass immigration reform, if we don't get it off the table in a reasonable practical way, it doesn't matter who you (Republicans) run in 2016," Graham said on ABC's "This Week" program. "The only way we can get back in the good graces of the Hispanic community, in my view, is to pass a comprehensive immigration reform." (Reporting by Lucia Mutikani and Margaret Chadbourn; Editing by David Brunnstrom)