The Bill, Hillary & Chelsea Clinton Foundation's flagship health program conceded earlier this year it had misreported by millions of the dollars the money it was given by governments compared with non-government donors in its tax returns for 2012 and 2013.
The charities have come under intense scrutiny this year with Hillary Clinton remaining the favorite to become the Democratic Party's nominee in the November 2016 presidential election.
The Clinton Health Access Initiative (CHAI) originally said it was amending the forms, known as form 990s, after Reuters discovered the errors in the spring. This week, CHAI said it had decided against refiling, saying the errors had "no material impact," CHAI spokeswoman Maura Daley said.
The Republican National Committee disagrees, its chairman, Reince Priebus, said on Tuesday in his letter to IRS Commissioner John Koskinen, a copy of which was given to Reuters.
"The American people deserve to know whether the largest philanthropic arm of the Clinton Foundation continues to misreport the funds it receives from foreign governments, and whether this might lead to the potential for further conflicts of interest," Priebus wrote.
Daley declined to comment beyond repeating that CHAI "does not believe a refiling is necessary." CHAI says the total amount of income was correctly reported for both years, but the breakdown of government against non-government funding had been muddled up.
Spokesmen for Hillary Clinton did not respond to requests for comment.