RZESZOW, Poland—President Biden traveled to a Polish city that has developed into a principal hub for Western military aid to Ukraine, signaling U.S. determination to support Kyiv with high-tech weaponry to punish Moscow for its invasion.

Mr. Biden met with U.S. troops, humanitarian workers and his Polish counterpart, Andrzej Duda, a day after both leaders attended a North Atlantic Treaty Organization summit where members pledged to reinforce the alliance’s eastern flank, provide further military support to Ukraine and impose high economic costs on Russia for its attack that began on Feb. 24.

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