Mr. Cuomo’s plan will be far more restrictive than the laws in Colorado or California, where medical marijuana is available to people with conditions as mild as backaches. It will allow just 20 hospitals across the state to prescribe marijuana to patients with cancer, glaucoma or other diseases that meet standards to be set by the New York State Department of Health.

While Mr. Cuomo’s measure falls well short of full legalization, it nonetheless moves New York, long one of the nation’s most punitive states for those caught using or dealing drugs, a significant step closer to policies being embraced by marijuana advocates and lawmakers elsewhere…

Mr. Cuomo’s change of heart comes at an interesting political juncture. In neighboring New Jersey, led by Gov. Chris Christie, a Republican whose presidential prospects are talked about even more often than Mr. Cuomo’s, medical marijuana was approved by his predecessor, Jon S. Corzine, a Democrat, but implemented only after Mr. Christie put in place rules limiting its strength, banning home delivery, and requiring patients to show they have exhausted conventional treatments. The first of six planned dispensaries has already opened.