Current rules require the votes of two-thirds of the Senate to bring legislation to the floor. With the chamber evenly divided between Democratic and Republican lawmakers, some Democrats want to change the rules to allow a bill to advance with a simple majority so that they can enact a voting-rights package opposed by Republicans.

Manchin, a conservative Democrat from a heavily Republican state, has said he won't agree on a rules change without seeing some Republican support for the measure.

"We need some good rules changes, and we can do that together. But you change the rules with two-thirds of the people that are present, so it's Democrats and Republicans changing the rules to make the place work better," he said.

"Getting rid of the filibuster does not make it work better."