WASHINGTON — Trump administration officials predicted big gains for the economy from a newly announced trade deal with China, but the economic losses sustained during a bruising 19-month trade war will not be easy to make up.

In a televised interview on Sunday, President Trump’s top trade negotiator praised the progress that the agreement between the world’s two biggest economies would make on issues like intellectual property, currency and financial services. He described the deal as “remarkable” and predicted that it would roughly double American exports to China by 2021.

Yet the negotiator, Robert Lighthizer, admitted that the limited agreement, which the administration says is just the first of several phases, was only a partial victory. He said it would leave many of the existing tariffs between the countries in place and other bigger changes to the Chinese economy undone.

“This is a first step in trying to integrate two very different systems, to the benefit of both of us,” Mr. Lighthizer, the United States trade representative, said in an interview on CBS’s “Face the Nation.” Anyone who thinks you would change China in one stroke of the pen “is foolish,” he said, adding: “The president is not foolish. He is very smart.”