Republican senator Rand Paul of Kentucky has become the first member of the Senate to test positive for the coronavirus, he has announced.

A statement on his Twitter account read: "Senator Rand Paul has tested positive for COVID-19. He is feeling fine and is in quarantine. He is asymptomatic and was tested out of an abundance of caution due to his extensive travel and events. He was not aware of any direct contact with any infected person.

"He expects to be back in the Senate after his quarantine period ends and will continue to work for the people of Kentucky at this difficult time. Ten days ago, our DC office began operating remotely, hence virtually no staff has had contact with Senator Rand Paul."

The diagnosis comes days after his father – former senator and presidential candidate Ron Paul – suggested that the crisis was a hoax.

Ron Paul wrote on his website: "People should ask themselves whether this coronavirus 'pandemic' could be a big hoax, with the actual danger of the disease massively exaggerated by those who seek to profit – financially or politically – from the ensuing panic."

He referred to Dr Anthony Fauci, the top health expert leading administration efforts to cope with the virus, as a "fearmonger".

Rand Paul joins two of other members of Congress — congressmen Mario Diaz-Balart and Ben McAdams — to test positive for the virus.

The Kentucky senator was the only senator to vote against bipartisan $8bn emergency relief legislation earlier this month.

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He also reportedly delayed a round of votes on another piece of coronavirus legislation in the Senate this week after forcing an unwieldy amendment that would "require a Social Security number for purposes of the child tax credit, and to provide the president the authority to transfer funds as necessary, and to terminate United States military operations and reconstruction activities in Afghanistan".

Mr Paul was criticised for appearing to call undocumented immigrants "non-people" after he said that only a "legitimate person" should be eligible for government assistance, and that one "should have to be a person to get taxpayer money".

The senate measure was intended to fund free coronavirus testing, paid emergency leave, unemployment insurance, Medicaid funding and other emergency measures.

Senate Minority Leader Chuck Schumer called the amendment a "colossal waste of time" before senators convened through the weekend to reach a deal on a stimulus package.

House Speaker Nancy Pelosi, however, said congressional Democrats would craft their own legislation over concerns that a Senate version would prioritise corporate bailouts. The Senate is preparing for a procedural vote on Sunday.