Lamar Alexander and Bob Corker were joined by Democrats Ben Cardin of Maryland and Doug Jones of Alabama when they introduced the resolution on Tuesday in the Senate.
About 1,300 black sanitation workers went on strike after two colleagues were fatally crushed by a malfunctioning garbage truck Feb. 1, 1968.
King came to Memphis to support the strike. He led a march on Beale Street that turned violent. He planned another march but he was fatally shot at the Lorraine Motel on April 4, 1968.
U.S. Rep. Steve Cohen introduced a similar resolution in the House on Jan. 30.
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