BERLIN—A furor in Europe over new reports of National Security Agency surveillance is undermining U.S. efforts to move beyond the affair and has thrown plans for a trans-Atlantic trade agreement into question just weeks before talks are scheduled to resume.

U.S. officials have engaged in a diplomatic offensive in recent weeks aimed at putting European fears over the data collection to rest. But a wave of European media reports based on information provided by former intelligence contractor Edward Snowden have provided further details of the U.S. surveillance programs, confounding Washington's efforts.

Tensions worsened Friday after the disclosure of a recorded phone conversation in which a top State Department official made derogatory comments about the European Union to a colleague.

Officials on both sides of the Atlantic say privately the NSA spying dispute in particular is weighing heavily on the already complicated negotiations over a trans-Atlantic trade deal, known officially as the Transatlantic Trade and Investment Partnership, or TTIP.

European leaders initially had high hopes for an agreement, which they believed could breathe life into the region's stagnant economy. But some senior officials now fear that the negotiations, which began last year and are set to resume next month in Brussels, will stall over data privacy and other issues that have come to light as a result of the spying affair.