WASHINGTON—House Republicans passed a $631 billion extension of the tax cuts they enacted in 2017, reprising their biggest legislative success of the past two years as they try to avoid losing their majority in the Nov. 6 election.

The legislation, which passed on a 220-191 vote, was part of a three-bill package that Republicans dubbed “Tax Reform 2.0.” On Thursday, they passed bills to expand retirement-savings incentives and tax breaks for startup businesses, picking up some Democratic support for those narrower measures.

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