By Ted Siefer

MANCHESTER, N.H. (Reuters) - Republican U.S. Senator Rand Paul took aim in New Hampshire on Wednesday at Common Core national education standards as he looked to strengthen ties with voters in the first-in-the-nation primary state before an expected 2016 White House run.

With its libertarian leanings, New Hampshire is seen as hospitable territory for Paul's small-government beliefs. His father, former Texas U.S. Representative Ron Paul, finished second in the 2012 New Hampshire primary, trailing only former Massachusetts Governor Mitt Romney, who went on to clinch the nomination.

A running theme during Paul's visit to the state on Wednesday was his critique of the federal government's involvement in grade-school education and particularly the Common Core standards adopted by most states and supported by President Barack Obama's administration.

The Kentucky lawmaker told staff and parents at a Manchester charter school that he would rather see local schools develop their own standards, which he argued would encourage innovation.

"If you have a national curriculum and rules, you'll never get to these new ideas," Paul said.

Paul's position against Common Core distinguishes him from former Florida Governor Jeb Bush, the Republican who has come closest to officially declaring his presidential candidacy and who has expressed support for the standards.

The Common Core English and math standards are aimed at boosting critical-thinking skills and unifying state guidelines.

But they have come under fire across the political spectrum. Left-leaning groups argue they increase reliance on standardized testing and discourage creativity and flexibility in the classroom. Some conservative groups say they amount to a federal takeover of education.

Paul added that if elected, he would eliminate the U.S. Department of Education, a sentiment that drew applause from the audience.

He also addressed another issue dear to many New Hampshire Republicans: gun rights. He spoke at a closed meeting for Second Amendment supporters at the Londonderry Fish and Game Club.

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Outside that event, Anthony Nino Jr., 49, said he liked Paul and his father for their commitment to individual rights.

"I think we need more people with his sense of duty to the Constitution," said Nino, wearing a hand-made three-corner hat, a style popular in colonial times. "If they have a duty to follow and enforce the Constitution, then they will respect another person's rights."

(Editing by Scott Malone and Peter Cooney)