WASHINGTON -- Republicans called on Senate Majority Leader Harry Reid to resign his leadership post over remarks he made in 2008 about then-presidential candidate Barack Obama, adding to the Nevada Democrat's political troubles.

Mr. Reid, who supported Mr. Obama's candidacy, said in private remarks during the campaign that the country was ready for a "light-skinned" African-American president with "no Negro dialect, unless he wanted to have one." The remarks are recounted in a new book, "Game Change: Obama and the Clintons,...