WASHINGTON — Realizing that his presidency could face potentially crippling questions over conflicts of interest, Donald Trump and his family are rushing to resolve potential controversies — by shuttering foundations and terminating development deals — even as the president-elect publicly maintains no legal conflicts exist.

The list of actions contemplated — with some already executed — is long, but the planned dissolving of the Donald J. Trump Foundation might be the most resonant, given the enormous controversies surrounding the nonprofit, which is under investigation by the New York attorney general.

Trump released a statement Saturday that he intends to dissolve that foundation. But a spokeswoman for the New York state attorney general’s office said Saturday that any move to close it required state approval, given the ongoing investigation into how the foundation spends its money and courts donations and given the state’s order that it stop fund-raising.

“The Trump Foundation is still under investigation by this office and cannot legally dissolve until that investigation is complete,’’ Amy Spitalnick, the press secretary, said.

In recent days, the president-elect and his aides had said he intends to distribute the assets of his personal charity and then close it down. He has examined a plan to hire an outside monitor to oversee the Trump Organization and has terminated some international business projects.

“This is a process that my father and my family are taking incredibly seriously,’’ said Eric Trump, who will help oversee the Trump Organization and who announced last week he was terminating fund-raising for his own charity, the Eric Trump Foundation.

Even with these steps, Donald Trump will enter the White House with a maze of financial holdings unlike those of any other president in US history. Many ethics experts still say the only way he can eliminate his most serious conflicts is to liquidate his company, and then put the money into a blind trust — a move the president-elect has so far rejected as impractical and unreasonable.

The potential roles that his daughter Ivanka Trump and her husband, Jared Kushner, may play in the administration are particularly vexatious. Both have business operations that could benefit from their government roles — even if they are not involved in the businesses on a day-to-day basis. Ivanka Trump’s business is so tied to her name that any position she might take in the White House or informal role she might play as an adviser to her father could benefit her company, which she will still own.

And because Donald Trump refuses to release his tax returns, the extent of his potential conflicts remains unknown.

“Yes, it would be hard to sell the business — there would be some personal discomfort,’’ said Robert Weissman, the president of Public Citizen, a liberal nonprofit group that has mocked Trump’s efforts to “drain the swamp’’ of Washington special interests. “But he ran for president of the United States and won, so those considerations can’t be weighted very heavily.’’

The hurried effort to clean up some of the family’s potential conflicts stands in contrast to the public statements by Trump since his election that as president he would not be subject to conflict of interest laws and could eliminate most questions by turning his business operations over entirely to his children.

But in recent weeks, as public scrutiny of the president-elect’s global business operations has intensified, Trump, his family, their executives in New York, and a team of outside lawyers have been working to eliminate many of these potential flashpoints — a task so complicated that Trump had delayed announcing the details.

Trump gave little thought to what to do with his business in the event of a victory on Election Day. But embarrassing reversals by his children highlighted concerns that access to the incoming administration could be for sale and pressed the family to respond.

A charity auction for coffee with Ivanka Trump, his daughter, was canceled, and Eric Trump and Donald Trump Jr., the president-elect’s sons, pulled out of another charity event that asked donors to give as much as $1 million in return for access to their father and a hunting expedition with his sons.

In interviews late last week, executives at the Trump Organization, advisers on the Trump transition team, and members of Donald Trump’s family said they were determined to move aggressively in the remaining days before the inauguration to clear as many of these potential conflicts as possible.