A week after Inauguration Day, the Democrats’ report said, a Flynn deputy for Middle East and North African affairs, Derek Harvey, met with the IP3’s co-founders at the White House, and asked National Security Council staff to include information about the nuclear power plan in a briefing to prepare Mr. Trump for a call with King Salman of Saudi Arabia.

The speed with which Mr. Harvey acted, and his circumvention of the normal scrutiny by experts across the government — like officials in the Energy and State Departments — prompted at least some National Security Council officials to raise concerns with Mr. Harvey, the report said. Eventually, ethics lawyers also raised concerns.

Even after Mr. Flynn left the White House in February 2017 under scrutiny by the F.B.I. for his communications with Russia, officials on the National Security Council continued to push ahead, repeatedly ignoring advice from the council’s ethics counsel, the report said.

At a March 2017 meeting, Mr. Harvey tried to revive the IP3 plan “so that Jared Kushner can present it to the president for approval,” the Democratic report said, a reference to Mr. Trump’s son-in-law and top adviser. Eventually Mr. Flynn’s successor, H. R. McMaster, said all work on the plan should cease because of potentially illegal conflicts.

The draft memos sent by IP3 to Mr. Flynn also referenced another close Trump associate, Thomas J. Barrack Jr., a businessman with deep ties to the Middle East who served as chairman of the president’s inaugural committee. In one memo from Mr. Flynn to Mr. Trump, the national security adviser advocated that Mr. Barrack be named a special representative to carry out the nuclear plan. Another memo, written as if it was from Mr. Trump to cabinet secretaries and other military and intelligence officials, directed federal agencies to support Mr. Barrack’s efforts.

The Democrats’ investigation comes at a sensitive time, when lawmakers of both parties are incensed over the Trump administration’s reluctance to punish Prince Mohammed bin Salman and the Saudi government over the killing of the Washington Post journalist Jamal Khashoggi. As supporters of the nuclear deal maneuvered in the opening days of the Trump White House, Mr. Kushner was orchestrating what would be Mr. Trump’s first overseas trip as president, to Saudi Arabia, and met on his own with the deputy crown prince at the time, Mr. bin Salman, before the prince became the power behind the Saudi throne.

Mr. Kushner’s efforts continue. He is scheduled to travel to the region next week, with a stop in Riyadh, the Saudi capital, to brief diplomats on the economic portions of the Trump administration’s Middle East peace plan.