WASHINGTON—The House passed legislation Thursday to ease trade pacts through Congress, as Republicans and some Democrats revived hopes for President Barack Obama’s trade agenda less than a week after liberals sank a similar bill.

The House’s 218-208 vote sends the measure to the Senate where Majority Leader Mitch McConnell (R., Ky.) wants to pass the bill as soon as next week. Fast-track authority would give Mr. Obama the power to submit trade deals to Congress for an up-or-down vote, without amendments.

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