WASHINGTON, Aug 17 (Reuters) - U.S. Democrats said Tuesday they would seek to advance another voting rights measure in the House of Representatives with the hopes of breaking a Senate logjam on the issue, but the odds of doing so remained long. Democrats want to pass federal voting rights legislation to try to counteract a wave of voting restrictions passed by Republican-led state legislatures. But Senate Republican Leader Mitch McConnell has said voting rules should be left to the states. House Democrats announced Tuesday they were introducing a bill to restore key protections of the Voting Rights Act of 1965, which outlawed discriminatory voting practices. The bill is named after the late Representative John Lewis, a civil rights icon who died last year. A House vote is expected Tuesday. The U.S. Supreme Court struck down portions of the Voting Rights Act in 2013 and again in 2021. The bill would seek to redress the court"s objections with an updated formula for which jurisdictions are subject to additional federal scrutiny, said a statement from the sponsor, Representative Terri Sewell. Another voting reform bill has been passed by the House but was blocked by Senate Republicans in June. Senate Majority Leader Chuck Schumer said last week that the chamber, divided 50-50 along party lines, will consider more voting rights legislation in September. Reporting by Susan Cornwell Editing by Andy Sullivan and Nick Zieminski