(Reuters) -- The top Senate Republican urged Democrats Thursday to set aside a bill aimed at stopping online piracy of movies and music, dealing yet another blow to controversial legislation that has pitted Hollywood against tech companies.

The Senate is scheduled to hold a procedural vote on the Protect IP Act on Tuesday. That measure, and the similar Stop Online Piracy Act in the House of Representatives, is aimed at curbing access to overseas Web sites that traffic in pirated content and counterfeit products.

But support for the bills has eroded over fears that legitimate web sites could also end up in legal jeopardy.

Rather than prematurely bringing the Protect IP Act to the Senate floor, we should first study and resolve the serious issues with this legislation, said Sen. Mitch McConnell of Kentucky, Republican leader in the Senate. I encourage the Senate majority to reconsider its decision to proceed to this bill.

Democrats have a majority in the Senate but bills need 60 votes to come up for debate so the legislation will need some Republican support to survive.

Earlier on Friday, a senior Senate Democratic aide acknowledged that the bill's backers did not have the votes to bring the measure to the floor to begin debate.

The momentum now is for killing the bill, the aide said.

But, the aide said, Sen. Patrick Leahy, D-Vt., chairman of the Senate Judiciary Committee, was working to craft a proposed compromise that could win Senate approval.

We should be able to go ahead and try to fix the bill. There is no reason that this bill can't be fixed through the legislative process, the aide said.

Some senators who had co-sponsored the legislation dropped their support on Wednesday as protests blanketed the Internet, turning Wikipedia and other popular web sites dark. Google, Facebook, Twitter and others protested the proposed legislation but did not shut down.

(Reporting by Diane Bartz; Additional reporting by Thomas Ferraro; Editing by Tim Dobbyn)