"Someone should look into who paid for the small organized rallies yesterday. The election is over!" the president tweeted Sunday morning.
That message came about an hour after an earlier tweet when he appeared to suggest the matter was a non-issue.
Trump has previously said Americans don't care about his returns.
"I did what was almost an impossible thing to do for a Republican-easily won the Electoral College! Now Tax Returns are brought up again?" Trump tweeted.
His messages came after thousands of protesters gathered Saturday in cities across America to pressure Trump to release his tax returns, a move of transparency he has repeatedly rejected.
The demonstrations were timed to coincide with the traditional April 15 deadline for annual tax filings, a key date on the calendar for US households, and resulted in dozens of arrests.
For decades, US presidents and presidential candidates have released their returns voluntarily, although there is no legal obligation to do so.
US law requires only the publication of a financial statement that estimates assets, including debt and revenue, but does not give details on the amount of taxes paid.
Trump, a billionaire property tycoon, released a financial statement but has kept his tax returns private, both during the election campaign and since taking office in January.
He argues that he cannot release them because he is being audited. But tax officials have said he can in fact release them if he so wishes.
Trump has on at least two previous occasions accused demonstrators of being paid to protest against him.
"Professional anarchists, thugs and paid protesters are proving the point of the millions of people who voted to MAKE AMERICA GREAT AGAIN!" he wrote on February 3 during protests against his executive order on immigration.
Watch: Pro and anti-Trump protests in US
