Two Democratic senators asked inspectors general at the Commerce and State Departments to investigate whether Trump administration officials violated ethics rules in a pair of multibillion-dollar deals involving the United Arab Emirates.

The call from the Senate Democrats came in response to an investigation published by The New York Times last week that examined the two Trump-era transactions with Emirati royals.

One of the deals involved a plan by the United States to allow the Emirates to import American-designed artificial intelligence computer chips, despite national security concerns among White House staff.

The other entailed a government-backed Emirati firm sending $2 billion to a cryptocurrency company created by the Trumps and the family of one of his advisers, Steve Witkoff. For the first six months of this year, Mr. Witkoff has formally served as a State Department employee, before transferring to a White House job.

“The pattern of these transactions is deeply troubling,” Senator Elizabeth Warren, Democrat of Massachusetts, and Senator Elissa Slotkin, Democrat of Michigan, wrote in the letter to the acting inspectors general at State and Commerce, as well as the Office of Government Ethics.

David Warrington, the White House counsel, said in a statement to The Times that “Mr. Witkoff, like all administration officials, takes seriously his compliance with the government ethics rules.”

While there was no evidence of an explicit quid-pro-quo agreement, The Times found that the two deals intersected in ways that were not publicly known when they were announced back to back in May. The Times examined the involvement of Mr. Witkoff and another White House adviser, David Sacks, a special government employee whose part-time status has allowed him to continue holding a private sector job as a venture capitalist.

Mr. Witkoff advocated sending chips to the Emirates at the same time that his family’s company was landing the crypto investment, even as White House colleagues argued that the U.A.E.’s close ties to China might compromise national security, The Times found.

Mr. Sacks’s role in the chip talks raised concerns from White House colleagues who believed it was improper for a working venture capitalist to negotiate deals that could benefit his industry. A spokeswoman for Mr. Sacks did not respond to a request for comment.

In a statement earlier this month, a White House spokeswoman said that there was no connection between the two deals, and that Mr. Witkoff was working with ethics officials to ensure full compliance with the rules. The statement said that Mr. Sacks had “no financial interest” in the chips deal with the U.A.E. He was granted an ethics waiver allowing him to participate in the discussions.

One open question is whether, in the current political environment in Washington, any kind of official review of the deals will occur. Democrats in Congress have repeatedly raised concerns about Mr. Trump’s business interests, especially in the crypto industry, without meaningful consequences.

Mr. Trump, in January, fired the State Department’s inspector general, Cardell K. Richardson Sr., as well as Jill Baisinger, who had been serving as acting inspector general at Commerce. Representatives for the state and commerce inspectors general, asked about the requests for the investigation, said in statements that they do not confirm or deny ongoing inquiries.

Federal criminal conflict of interest law prohibits government employees from playing a role “personally and substantially” in certain “matters where they have a financial interest.” This requirement extends to what the law refers to as “particular matters” that could benefit “their spouse, minor child, general partner, and certain other persons and organizations” that they own or work for.

A separate rule prohibits federal employees from using their public office, title, or authority for their own private gain or for the private gain of friends, relatives, or others with whom the employee is affiliated. The broad aim of this rule is to avoid “any actions creating the appearance that they are violating the law or the ethical standards.”

These rules apply to both full-time employees, such as Mr. Witkoff, as well as special government employees like Mr. Sacks. The president is exempt from these rules.

Three ethics lawyers interviewed by The Times said the questions about potential ethics violations are particularly relevant to Mr. Witkoff, who serves as Mr. Trump’s Middle East envoy, with a diplomatic portfolio that is more expansive than the title indicates. He also is a longtime friend of Mr. Trump’s.

Last year, Mr. Witkoff and his sons, along with Mr. Trump’s sons, founded World Liberty Financial, a crypto company. Mr. Witkoff, a real estate lawyer and investor, announced plans after he was appointed by Mr. Trump to sell his stake in his real estate company and other ventures, turning over much of his corporate holdings to his sons.

Mr. Warrington, the White House counsel, in his statement to The Times on Wednesday, said that Mr. Witkoff is “taking all the legal steps necessary to divest,” from those holdings, meaning he still has a financial interest in World Liberty.

That means he still was in a position to benefit financially when World Liberty struck the $2 billion deal with the Emiratis.

A financial disclosure report Mr. Witkoff signed last month that also listed these holdings did not detail how much Mr. Witkoff’s holdings are worth. But statements by World Liberty suggest that the Witkoff family has been allocated 3.75 billion of the company’s $WLFI tokens, which at the current trading price would be worth nearly $800 million.

Given that Mr. Witkoff still had a financial interest in World Liberty, he would be prohibited under federal criminal law from participating in government decisions that directly benefit this holding.

There is little that congressional Democrats can do to force the inspectors general to start an investigation. But lawmakers can still take symbolic steps targeting Mr. Trump and his allies over their ties to the crypto and A.I. industries.

“In the history of our country’s foreign policy, one is hard-pressed to find two senior officials with such significant conflicts of interest involved in decisions regarding national security,” Ms. Warren and Ms. Slotkin wrote in their letter to the inspectors general. “Such unbridled conflicts of interest have no place in the U.S. government.”

Separately, Senator Chris Van Hollen, Democrat of Maryland, said in a statement to The Times that he planned to use his position as top Democrat on a panel that oversees the Commerce Department’s budget to press for answers about the U.A.E. deals.

Last week, a group of Democrats also announced that they were examining whether Mr. Sacks had violated the rules governing special government employees, who are limited to working 130 days a year. (A White House spokeswoman previously told The Times that Mr. Sacks “continues to carefully manage” his days as a special government employee to ensure he stays under the limit.)

The same day, Representative Sean Casten, Democrat of Illinois, and Senator Jeff Merkley, Democrat of Oregon, sent a letter to the Securities and Exchange Commission, requesting information about Justin Sun, a crypto billionaire who has worked closely with the Trump family.

Mr. Sun was one of the largest investors in World Liberty Financial. Early in Mr. Trump’s second term, the S.E.C. paused a fraud lawsuit that it had filed against him.

“Part of this is making sure that we remind people who are in public service that we are in a democracy; parties change from time to time,” Mr. Casten said in an interview. “There will be oversight coming, there will be accountability coming.”