WASHINGTON — President Trump threatened on Tuesday to use federal tax law to penalize the National Football League over players who kneel in protest during the national anthem, but the White House later backed off, saying he was only making a point.

Escalating a political fight that has resonated with his conservative base, Mr. Trump said Congress should eliminate a law that allowed the N.F.L. central office to avoid paying taxes as a nonprofit entity. “Why is the NFL getting massive tax breaks while at the same time disrespecting our Anthem, Flag and Country?” he wrote on Twitter. “Change tax law!”

The tax break for the N.F.L. has been a point of controversy for years, and other conservatives have taken up the cause in recent weeks as the president has repeatedly assailed the league over the player protests. But the idea would be more about symbolism than impact. The tax break applies only to the central office, not the teams, which are the real moneymakers and already pay taxes as for-profit organizations, and the N.F.L. voluntarily gave up the office’s tax exemption in 2015.

At a news briefing later in the day, Sarah Huckabee Sanders, the White House press secretary, said the president was making a statement, not a proposal. She noted that professional football teams benefit when local and state governments help them build stadiums but did not suggest that Congress should try to block those lower governments from doing so.