The Russian government’s top investment manager, who has Harvard and McKinsey credentials and fluent English, brought a simple printout to Tuesday’s talks with the Trump administration in Saudi Arabia.

Its message: By pulling out of Russia in outrage over the invasion of Ukraine, American companies had walked away from piles of cold, hard cash.

“Losses of U.S. companies by industry,” read the document, which Kirill Dmitriev, the head of Russia’s sovereign wealth fund, showed to a New York Times reporter. “Total losses,” one of the columns said. The sum at the bottom: $324 billion.

In appealing to President Trump, the Kremlin has zeroed in on his desire to make a profit. President Vladimir V. Putin on Wednesday praised the U.S. delegation in Riyadh for not criticizing Russia as previous administrations did — there was no “condemnation of what was done in the past,” he said. He added that beyond geopolitics, the two countries were now moving toward deeper engagement on space, the economy and “our joint work on global energy markets.”

Sergey V. Lavrov, Russia’s foreign minister, said after Tuesday’s meeting that “there was great interest” in the room “in removing artificial barriers to the development of mutually beneficial economic cooperation” — an apparent reference to lifting American sanctions.

Remarkably, the Trump administration appears to be engaging with Russia’s message without demanding payment up front. After Ukraine suggested the possibility of natural resource deals to Mr. Trump, his treasury secretary pushed to have the country sign away half its mineral wealth. And Mr. Trump continues to portray American allies as freeloaders, threatening more tariffs and demanding they pay more for their own defense.

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