The US ambassador to the Netherlands, Pete Hoekstra, was quoted by the Dutch daily Financieel Dagblad on Friday as saying that the technology "does not belong in certain places", in an apparent reference to China.
He was responding to comments to the same newspaper by his Chinese counterpart Xu Hong warning about the "politicisation" of commercial ties between China and the Netherlands over the machine.
Washington and Beijing have been in a trade war for the last two years, although they signed a deal for a truce on Wednesday. The bus-sized Extreme Ultraviolet (EU) machine that ASML wants to export to China prints circuits on microchips at the smallest possible level permitted by current miniaturisation technology.