The flashy online announcement called it “the most EXCLUSIVE INVITATION in the World,” a chance to have “an intimate private dinner” with President Trump at his members-only golf club in Virginia, followed by a tour of the White House.

A seat would be reserved for each of the top 220 investors in $TRUMP, a cryptocurrency that Mr. Trump launched on the eve of his inauguration.

In an astonishing escalation of the Trump family’s efforts to profit from crypto, a website promoting $TRUMP, the president’s so-called memecoin, announced on Wednesday that the coin’s largest buyers would be invited to meet him. The effort was, in effect, an offer of access to the White House in exchange for an investment in one of Mr. Trump’s crypto ventures.

“Have Dinner with President Trump and the $TRUMP Community!” the invitation said. “Let the President know how many $TRUMP coins YOU own!”

For months, Mr. Trump’s forays into crypto have created ethical conflicts with little precedent in presidential history. As he markets digital currencies to the public, Mr. Trump has also appointed regulators who are scaling back crypto enforcement and called for legislation that would boost the industry’s prospects in the United States.

As news of the dinner invitation spread on social media, the memecoin’s price surged more than 60 percent, suggesting that investors were rushing to accumulate enough coins to qualify for a dinner seat.