AMSTERDAM — The scene at the 420 Cafe on a recent Friday was typical of what many travelers have come to associate with Amsterdam. Behind the bar, Janne Svensson, 34, a self-described “cannabis refugee” from Norway, weighed out small quantities of marijuana and hashish for her customers, many from foreign countries. They sat quietly, smoking and sipping coffee, as familiar strains of Jimi Hendrix drifted softly from the stereo and giant manta rays cavorted in a nature video on a big-screen television.

While there are many attractions that draw visitors to the Netherlands — including the friendly and straightforward people, world-class museums, charming architecture and elegant canal scenes — nearly a quarter of this city’s more than four million foreign tourists a year will visit its coffee shops, where the sale of small quantities of cannabis is tolerated.

But Amsterdam’s days as a destination for hazy holidays may be numbered. Prime Minister Mark Rutte’s right-wing coalition government is pushing to sharply restrict the operations of the coffee shops and to prohibit the sale of the drugs to nonresidents. If the measures survive a court challenge and the opposition of local officials, the first phase would begin May 1.

“I think that by the end of next year, there will be no drug tourism in the Netherlands,” Ard van der Steur, a Parliament member and a spokesman for Mr. Rutte’s People’s Party for Freedom and Democracy, said in an interview in The Hague. “We have created an incredible criminal industry that we need to get rid of.”