BRUSSELS — Denmark gave permission on Wednesday for a natural gas pipeline from Russia to Germany to pass through waters in its exclusive economic zone, meaning that the project, Nord Stream 2, can be completed despite sharp criticism from the United States, Ukraine and Poland.

With nearly all of its 2,400 kilometers of pipe already laid, Nord Stream 2, wholly owned by Russia’s Gazprom, should be completed roughly on schedule early next year. It is actually a pair of pipelines, complementing a previous pair, Nord Stream 1, and will double capacity to 110 billion cubic meters, or about 3.9 trillion cubic feet.

The pipelines are sensitive geopolitically, because they increase German and European dependence on Russian natural gas while bypassing Ukraine and Poland, cutting off some transit fees for those two economies. Some critics believe that Russia is trying to harm Ukraine’s economy in particular, especially after the 2014 annexation of Crimea and the continuing warfare in eastern Ukraine.