“We should get a move on,” the chancellor said. “We all know the reproaches, worries and fears, and what difficulties remain.”

But if time is used wisely, she said, an agreement that will raise living standards can emerge. “So my request to those who are present,” she added, looking around the audience of hundreds of business leaders and politicians, is: “Do it, and then we can have a great success this year.”

The chancellor greeted the president at the Schloss Herrenhausen, the former summer residence of the Royal House of Hanover. They stood in front of a line of German troops in gray overcoats and green berets as the national anthems of the two nations played before the two leaders returned inside for a private meeting.

Mr. Obama said he hoped the trade negotiations could be completed before he left office.

“I don’t anticipate that we will be able to complete ratification of a deal by the end of this year, but I do anticipate that we will have completed the agreement,” he said. Once negotiations are finished, he said, “people will be able to see exactly why this will be good for our two countries.”

Yet even as he expressed confidence that a deal would be reached this year, Mr. Obama acknowledged that “time is not on our side,” and he offered a thinly veiled warning that a deal could be doomed if politicians like Hillary Clinton, who opposes the accord, are elected this year.

“If we don’t complete negotiations this year, then upcoming political transitions in the United States and Europe could mean this agreement won’t be finished for quite some time,” Mr. Obama said, not mentioning Mrs. Clinton, his former secretary of state, directly.