WASHINGTON—U.S. efforts to address competition with China progressed on Tuesday when the chairman of the House of Representatives Foreign Affairs Committee introduced sweeping legislation to boost economic competitiveness and push Beijing on human rights. Rep. Gregory Meeks (D-N.Y.) introduced the “Ensuring American Global Leadership and Engagement Act,” or EAGLE Act, as the U.S. Senate separately heads toward a vote on its own legislative package seeking to counter China. The desire for a hard line in dealings with China is one of the few truly bipartisan sentiments in the deeply divided U.S. Congress, which is narrowly controlled by President Joe Biden’s fellow Democrats. The Biden administration supports efforts to counter China, with officials repeatedly listing competition with Beijing among their greatest strategic challenges. The 470-page bill introduced by Meeks addresses a range of issues, including increased investment to promote U.S. manufacturing, trade, work with allies and partners, re-engagement in international organizations, …