By Brett Forrest

Denmark granted unexpectedly swift approval for resuming construction of the Russian-backed Nord Stream 2 pipeline in Danish waters, potentially clearing one of the last hurdles for completing the project at the center of a geopolitical tussle.

The pipeline, once finished and certified, will deliver Russian natural gas to Germany, and while those two governments have characterized the project in commercial terms, U.S. lawmakers and officials fear that Nord Stream 2 will give Moscow greater political leverage across Europe.

U.S. sanctions put in place last year stalled construction of the pipeline in its last stretch, primarily on the Baltic seabed in Danish waters. Denmark generally prohibits vessels doing seabed construction to anchor on the seafloor, due to the presence of unexploded World War II ordinance, and Russia's pipe-laying vessels generally rely on anchoring, rather than using a computer-controlled system to maintain position.

Nord Stream 2 AG, a company owned by Russia's gas-export monopoly Gazprom to construct and manage the pipeline, petitioned the Danish regulator last month to use anchored vessels. The Danish Energy Agency granted the approval Monday, ahead of an end-of-July time frame earlier announced by a spokesman.

The Danish agency said in a statement that the remaining construction lies "outside the area where bottom trawling, anchoring and seabed intervention are discouraged due to the risk posed by dumped chemical warfare agents."

Obstacles to finishing the pipeline remain, including renewed efforts by the U.S. to impose new sanctions.

Denmark's faster-than-expected approval boosted a $9 billion project that Russia and Germany have championed, over objections from the U.S. and that will alter the energy map of Europe.

A spokesman for Nord Stream 2 AG said in a statement that the company is considering different options for proceeding.

Russian officials have been adamant that the pipeline will be completed despite obstacles, including U.S. attempts to stop it. Earlier this year, President Vladimir Putin estimated that work would be finished by the end of this year or early next year.

Nord Stream 2 will allow Russia partly to circumvent a pipeline transit system that runs through Ukraine and has handled gas deliveries for decades. Ukrainian officials have spent years lobbying against Nord Stream 2, worrying that it will weaken Ukraine against a stronger Russia, and Kyiv has found supporters in Washington.

Sen. Ted Cruz (R., Texas) and Sen. Jeanne Shaheen (D., N.H.) last year co-sponsored a bill that provided for the sanctioning of companies supplying technical assistance to Nord Stream 2 construction.

The principal target was Allseas Group SA, a Swiss company that supplied the main pipe-laying vessel. When this sanctions legislation passed into law in December, Allseas abandoned the project, and construction stalled.

Last month, the Senate approved a new Nord Stream 2 sanctions bill from Sens. Cruz and Shaheen, folding it into a larger defense authorization act. The Senate bill calls for sanctions against companies that provide certification, port facilities, tethering services or insurance to the project. The House is discussing a similar measure.

"All options remain on the table" to prevent Nord Stream 2's completion, a spokeswoman for Mr. Cruz said in a statement. She said that the proposed new legislation "makes clear those involved with vessels installing the pipeline or its certification will face crippling and immediate sanctions."

Officials on either side of the fray remain focused on this potential new round of sanctions and on the calendar.

Work on the 120 kilometers of pipeline to be constructed in Danish waters is projected to take roughly four months and can begin only after the Danish Energy Agency's appeal period expires on Aug. 3. An additional 30 kilometers of pipeline in German waters remains to be built.

The new sanctions are likely to be included in the National Defense Authorization Act, which is expected to be signed in November, according to a congressional aide.

If the legislation passes into law, insurers involved in the project "will need to stop immediately," said Vadym Glamazdin, an adviser to the CEO of Naftogaz, Ukraine's national oil-and-gas company.

Companies providing the licensing and certification necessary to make the pipeline operational may also likely choose to abandon it. "Without this certification, the pipeline cannot be used even if finished," Mr. Glamazdin said.

Write to Brett Forrest at brett.forrest@wsj.com