A reclusive billionaire, anti-tax crusader and major financial backer of Donald Trump has been named as the anonymous private donor who gave $130m to the government to help pay US troops during the federal shutdown that is now in its fourth week, according to the New York Times.

Timothy Mellon, heir to the gilded age industrialist and former treasury secretary Andrew Mellon, is the secret donor whom Trump has described as a “friend”, “great American” and “patriot”, but has refused to name, citing two anonymous sources familiar with the arrangement, the Times reported.

Trump first announced the secret, legally controversial donation on Thursday amid growing clamour about the potential financial hardship being caused by the ongoing federal shutdown on the 1.3 million active-duty military troops.

US defence officials confirmed the gift, which President Donald Trump said will make up for shortfalls in paying the country’s 1.32m service members, but declined to identify the donor, only dropping a few clues, and that he was “a big supporter of mine” and a US citizen.

The government shut down more than three weeks ago, after lawmakers failed to approve a funding deal. The Trump administration paid troops last week by shifting $8bn from military research, but it is unclear what will happen on the next payday at the end of the month.

The shutdown is poised to become one of the longest in US history.

The next military payday is scheduled for 31 October, at the end of this week.

Pentagon spokesman Sean Parnell told reporters on Friday that the donation “was made on the condition that it be used to offset the cost-of-service members’ salaries and benefits,” and it was allowed under the department’s “general gift acceptance authority”.

Most government workers have been furloughed, or in some cases, told to work without pay while the shutdown lasts.

While unusual, the Pentagon does sometimes accept gifts from donors, but they must be given to fund specific projects, such as a school, hospital, library, museum, or cemetery.

Critics questioned why the US military would accept anonymous funds.

“Using anonymous donations to fund our military raises troubling questions of whether our own troops are at risk of literally being bought and paid for by foreign powers,” said Delaware Senator Chris Coons, the top Democrat on the Senate’s defence appropriations subcommittee.