President Trump announced on Thursday that the United States intended to sign a trade deal with Britain that would bring the two nations closer and roll back some of the punishing tariffs he issued on that country’s products.

Both sides consider a trade pact deeply beneficial, and a deal has been under discussion since Mr. Trump’s first term. But the announcement on Thursday was scant on details, reflecting the haste of the Trump administration’s efforts to negotiate with more than a dozen nations and rework the global trading system in a matter of months.

The agreement, which Mr. Trump said would be the first of many, would include Britain’s dropping its tariffs on U.S. beef, ethanol, sports equipment and other products, and buying $10 billion of Boeing airplanes. The United States in return said it would pare back tariffs that Mr. Trump has put on cars and steel, though it will leave a 10 percent levy in place for all British exports.

Neither government has said when they expect the agreement to be finalized. A document released by the Trump administration on Thursday evening listed half a dozen general priorities, and said the countries would immediately begin negotiations “to develop and formalize” them.

The British government said it was still pushing to bring down the 10 percent tariff on most other goods. American officials said they would push Britain to reconsider a tax on technology companies. Officials from both governments will need to meet in the coming months to hammer out more specific language, leaving open the potential for disagreements.

Nevertheless, the leaders of both nations hailed their cooperation in joint announcements on Thursday that invoked the deep relationship between their countries. Speaking from the Oval Office, with Prime Minister Keir Starmer of Britain on speakerphone, Mr. Trump called it a “great deal for both countries.” Mr. Starmer noted that it was the 80th anniversary of the Allies’ victory in Europe in World War II.