By Patricia Zengerle

WASHINGTON, June 12 (Reuters) - U.S. senators said on Monday they were close to an agreement on legislation imposing new sanctions on Russia, including a possible provision that would prevent the White House from easing sanctions without congressional approval.

Democrats and Republicans on the Foreign Relations and Banking Committees have been negotiating for about a week on an amendment to an Iran sanctions bill that also would impose sanctions to punish Russia over issues including its alleged meddling in the 2016 U.S. election, annexation of Ukraine's Crimea region and support for the government of Syria in that country's six-year-long civil war.

The Iran bill could come up for a vote as soon as this week.

Senate Republican Majority Leader Mitch McConnell said on Monday that lawmakers still were working on "additional and much-needed sanctions on Russia."

Senators declined to comment publicly on what would be in the final bill but proposals under consideration included putting existing sanctions imposed by presidential executive order into law and imposing additional sanctions that might include some on Russia's energy sector. They also could include creation of a process that would require Congress to review, and potentially block, any effort by the White House to ease sanctions on Russia.

Senator Ben Cardin, the top Democrat on the Senate Foreign Relations Committee, told reporters earlier on Monday that an agreement could be announced as soon as late Monday or Tuesday.

In December, the final full month of President Barack Obama's administration, the United States sanctioned Russian businessmen and companies for Moscow's role in Ukraine. (Reporting by Patricia Zengerle; Editing by Bill Trott)