Rand Paul greets supporters after speaking at the Galt House Hotel in Louisville, Kentucky, yesterday. Photograph: William DeShazer/New York Times

Republican Rand Paul, the libertarian conservative senator, has declared a plan to take America back from an unpopular Washington establishment in announcing his candidacy for the presidency in 2016.

In a speech to a hotel ballroom full of raucous supporters in Louisville in his home state of Kentucky, the first-term senator set out a vision to appeal to a coalition of civil libertarians, fiscal conservatives and anti-war proponents on the fringe of the Republican Party.

Tapping the unpopularity of Washington by railing against the special interests of the political establishment and big government, Paul painted himself as an outsider, blaming Republicans and Democrats for the problems in the US.

The Christian senator took the stage at the Galt House hotel on the banks of the Ohio River to the strains of 1970s rock music and stood before a campaign banner slogan: Defeat the Washington machine; unleash the American dream.

The anti-establishment senator, a household political name since his nearly 13-hour filibuster in the US Senate about drone attacks on American citizens in 2013, is the second Republican to declare his candidacy, following another freshman senator, Ted Cruz of Texas.

Paul (52), a former ophthalmologist, will benefit from a base built by his father, Ron (79), the former Texas congressman who ran for the presidency three times and electrified a well-organised grassroots network of young libertarians, many of whom were new to politics.

Those supporters, who backed Ron Pauls isolationist foreign policy, have been less easy with the younger Paul, who has generally opposed military intervention but who said last year that war was a last resort and recently proposed a $190 billion (175 billion) increase in defence spending.

Entering the presidential race early, with 580 days to election day, Paul sought to challenge the perception that he is isolationist on foreign policy or weak-kneed on national security. He said: Conservatives should not succumb to the notion that a government inept at home will somehow succeed at building nations abroad.

I envision an America with a national defence unparalleled, undefeatable and unencumbered by overseas nation-building.

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Rand Paul enters 2016 US presidential race with battle cry to take America back