Trump says his two oldest sons, other executives will handle his businesses during presidency

President-elect Donald Trump said late Monday that his two eldest sons Don Jr. and Eric — along with selected executives — would oversee Trump's businesses during his term of office.

Trump made the announcement in a series of tweets hours after his transition team had postponed a scheduled Thursday press conference at which the president-elect was due to discuss the Trump Organization and his other financial holdings.

In another tweet, Trump promised that he would hold a press conference "in the near future to discuss the business, Cabinet picks and all other topics of interest."

A specific date for the rescheduled press conference was not immediately announced, but a transition source told Fox News earlier Monday that it was likely to take place next month due to the flurry of activity surrounding Trump's Cabinet picks.

Sean Spicer, a Trump transition team spokesman, told the Associated Press that legal teams need more time to work out the plan for the Trump Organization.

Trump's announcement also opens the door for his daughter, Ivanka, to take a position in the new administration, since she would not be involved in running the Trump Organization.

Trump's transition team has faced a number of questions about potential conflicts of interest between his expansive financial holdings and the decisions that will reach his desk as president. Some details of Trump's finances are unknown given that he never released his tax returns during the presidential campaign, breaking decades of precedent.

Trump's tweets late Monday did not mention whether he would divest himself of his ownership stake in the Trump Organization.

For decades, presidents have sold their stocks and other personal holdings and put the cash into a blind trust overseen by an investment manager.

Trump has ownership stakes in residential towers, hotels, resorts and golf clubs in the U.S., and has struck licensing and property management deals for similar properties around the world. In a financial disclosure he was required to file during the campaign, he listed stakes in about 500 companies in at least 25 countries.

Only by selling to an uninterested third party can Trump assuage critics who suggest that otherwise he could shape regulatory, tax or foreign policies to enrich himself. A sale would also prevent people from trying to influence policies by helping -- or threatening to hurt -- his business.

Few are expecting Trump to make a clean break.

Former House Speaker Newt Gingrich, a vice chairman of Trump's transition team, has said voters knew Trump was a billionaire businessman when they elected him and he shouldn't have to sell. Instead, Gingrich said he recommended to transition officials that Trump appoint a panel of five ethics "jurists" to vet potential conflicts.

The government agency charged with monitoring ethics is pushing for far more. The Office of Government Ethics tweeted recently about Trump, "We can't repeat enough how good this total divesture will be." The office clarified later that it did not know if that was indeed his plan.

Fox News' John Roberts and Serafin Gomez contributed to this report. The Associated Press contributed to this report.