WASHINGTON  Telecommunications companies won a skirmish in the Senate on Monday as a bill to protect them from lawsuits for cooperating with the Bush administration’s eavesdropping programs easily overcame a procedural hurdle.

By 76 to 10, with Democrats divided, the Senate voted to advance the bill for consideration. A measure to block it, which was led by Senator Christopher J. Dodd, Democrat of Connecticut fell short, as those who wanted the bill to reach the floor got 16 votes more than the 60 needed to achieve that goal.

What happens next is not immediately clear. A different bill, which would not grant immunity to the companies, was also expected to be introduced by Senator Patrick J. Leahy, the Vermont Democrat who heads the Judiciary Committee. And whatever bill emerges from the Senate may have to be reconciled with a House version that does not include immunity.

The measures are meant to renew the Foreign Intelligence Surveillance Act, legislation that has deeply divided the White House and Capitol Hill and members of the House and Senate. Some action is necessary fairly soon, because the current FISA law expires in February.