Mr. Pence said pointedly that while some NATO members met the spending goal, “many others, including some of our largest allies, still lack a credible path.” Mr. Trump, he said, “expects allies to meet that goal. For most that means the time has come to do more.”

Applause for Mr. Pence’s speech was thin. Chancellor Angela Merkel of Germany, who spoke before the vice president, had argued that increases in military spending must be gradual to be efficient and effective.

Mrs. Merkel said that spending on other matters — like development aid, education for girls and women, and caring for refugees — also contributes to mutual security, as do stronger multilateral institutions like the European Union and the United Nations, which Mr. Trump has criticized.

Europe needs the support of the United States in the face of Islamist terrorism and Russian ambition, Mrs. Merkel said, promising to continue to spend more to meet NATO goals. “We need the military strength of the United States,” she said.

But she warned against nationalism, without specifically mentioning Mr. Trump’s “America First” philosophy. “Will we be able to continue working well together, or will we all fall back into our individual roles?” she asked. “Let’s make the world better together, and then it will be better for each of us.”