WASHINGTON — As President Trump has struggled to explain the difficulty of negotiating a trade agreement with China, he has embraced a side argument: A Democratic president would only agree to a worse deal.

But not just any Democratic president.

“China is DREAMING that Sleepy Joe Biden, or any of the others, gets elected in 2020,” Mr. Trump wrote on Twitter Sunday. “They LOVE ripping off America!”

By Monday afternoon, Mr. Biden, making his first trip to New Hampshire since entering the 2020 race, was happily returning fire, criticizing the Twitter-borne blur of threats and flattery Mr. Trump had aimed at Beijing. “He’s going about it all the wrong way, a lot of bravado, no action,” the former vice president told reporters.

It is just the sort of fight Mr. Biden has been spoiling for: a head-to-head contest with the incumbent on an issue that elevates Mr. Biden into a statesmanlike role, well above the Democratic primary fray and all the sniping candidates and liberal litmus tests therein.