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

In recent days, the president-elect and his aides have said that he intends to distribute the assets of his personal charity and then close it down, 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 that he was terminating fund-raising for his own charity, the Eric Trump Foundation.

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