On Tuesday night, Ryosei Akazawa, the Japanese trade negotiator, sat across from President Trump’s desk in the Oval Office, clustered alongside the U.S. secretaries of Treasury, commerce and state, trying to convince the president to back off from the punishing tariff rates he had threatened on Japan.

As a carrot, American and Japanese negotiators offered Mr. Trump an extraordinary proposal: Japan would create a $400 billion investment fund that Mr. Trump himself could decide where to invest, with half of the profits flowing to the U.S. government.

The fund represented a significant expansion by the president over domestic investment, an idea that pleased Mr. Trump. He set about renegotiating some of the terms, crossing out numbers and scribbling on a placemat-size visual aid brought to the meeting by Howard Lutnick, the commerce secretary. In the end, Mr. Trump upped the ante and announced that Japan, already the country’s largest foreign investor, would create a fund of $550 billion to invest in the United States, with the U.S. government receiving 90 percent of the profits.

The announcement has raised significant questions about whether that investment will materialize, and how the president will decide where to direct the funds. But the provision appears to be the key way that Japan — which was reluctant to open its agricultural markets to U.S. exports and insistent on lowering Mr. Trump’s tariffs on cars — was able to convince the president to agree to a trade deal.

It is also another novel approach to economic policymaking by Mr. Trump, who has smashed Washington’s conventional wisdom on trade and taken an expansive view of the control presidents should have over the economy.

Karoline Leavitt, the White House press secretary, on Wednesday described the investment as the “centerpiece” of the trade deal with Japan. She said the funds would be spent “at President Trump’s discretion and direction into key industries such as energy, semiconductors, critical minerals, pharmaceuticals and shipbuilding.”