The United States issued a stern warning to Romania on Monday as thousands took to the streets on Bucharest to protest moves to sideline an anti-graft agency.

Romania's parliament is reviewing legislation that would overhaul the judicial system and reduce the powers of the DNA anti-corruption directorate.

The moves have already raised the ire of trade unions and civil society groups at home, and now Washington has added its diplomatic voice to the swelling protests.

State Department spokeswoman Heather Nauert said the US administration regarded the draft law "with concern."

As proposed, she said, the government's move "could undermine the fight against corruption and weaken judicial independence in Romania.

"This legislation ... threatens the progress Romania has made in recent years to build strong judicial institutions shielded from political interference.

"We urge the parliament of Romania to reject proposals that weaken the rule of law and endanger the fight against corruption," she said.

Earlier, between 15,000 and 25,000 Romanians had marched in the capital to denounce the proposals, with thousands more coming out around the country.