Edward G. Rendell, a former Democratic governor of Pennsylvania, said the foundation should be disbanded if Mrs. Clinton wins, and he added that it would make sense for the charity to stop taking foreign donations immediately.
“I think they’ll do the right thing,” Mr. Rendell said, “and the right thing here is, without question, that the first gentleman have nothing to do with raising money for the foundation.”
Mr. Minassian said ending foreign fund-raising before other sources of money could be found, and without knowing who will win the election, could needlessly gut programs that help provide, for instance, H.I.V. medication to children in Africa.
Begun in 1997, the foundation has raised roughly $2 billion and is overseen by a board that includes Mr. Clinton and the couple’s daughter, Chelsea. Mrs. Clinton joined when she left the State Department and stepped down in 2015 before beginning her campaign. Its work covers 180 countries, helping fund more than 3,500 projects.
Having a former president at the helm proved particularly productive, with foreign leaders and business people opening their doors — and their wallets — to the preternaturally sociable Mr. Clinton.
Among the charity’s accomplishments: Its Clinton Health Access Initiative — which is run by Ira C. Magaziner, who was a White House aide involved in Mrs. Clinton’s failed effort to overhaul the health care system in her husband’s first term — renegotiated the cost of H.I.V. drugs to make them accessible to 11.5 million people. The foundation helped bring healthier meals to more than 31,000 schools in the United States, and it has helped 105,000 farmers in East Africa increase their yields, according to the foundation’s tally.
In December 2008, shortly before Mrs. Clinton became secretary of state, Mr. Clinton released a list of more than 200,000 donors to defuse speculation about conflicts.
Soon after, Mrs. Clinton agreed to keep foundation matters separate from official business, including a pledge to “not participate personally and substantially in any particular matter that has a direct and predictable effect upon” the foundation without a waiver. The Obama White House had particularly disliked the gatherings of world leaders, academics and business people, called the Clinton Global Initiative, that the foundation was holding overseas. The foundation limited the conferences to domestic locations while Mrs. Clinton was secretary of state. On Thursday, Mr. Clinton said the gathering in September in New York would be the foundation’s last.
One of the attendees at these conferences speaks to the stickiness of some donor relationships.
Victor Pinchuk, a steel magnate whose father-in-law, Leonid Kuchma, was president of Ukraine from 1994 to 2005, has directed between $10 million and $25 million to the foundation. He has lent his private plane to the Clintons and traveled to Los Angeles in 2011 to attend Mr. Clinton’s star-studded 65th birthday celebration.
Between September 2011 and November 2012, Douglas E. Schoen, a former political consultant for Mr. Clinton, arranged about a dozen meetings with State Department officials on behalf of or with Mr. Pinchuk to discuss the continuing political crisis in Ukraine, according to reports Mr. Schoen filed as a registered lobbyist.
“I had breakfast with Pinchuk. He will see you at the Brookings lunch,” Melanne Verveer, a Ukrainian-American then working for the State Department, wrote in a June 2012 email to Mrs. Clinton.
On the Trail: The Week of Aug. 14
CreditDamon Winter/The New York Times
A previously undisclosed email obtained by Citizens United, the conservative advocacy group, through public records lawsuits shows the name of Mr. Pinchuk, described as one of Ukraine’s “most successful businessmen,” among those on an eight-page list of influential people invited to a dinner party at the Clintons’ home.
Earlier in 2012, Ambassador John F. Tefft wrote to Mrs. Clinton about a visit to Ukraine by Chelsea Clinton and her husband, Marc Mezvinsky, “at the invitation of oligarch, Victor Pinchuk.” Mrs. Clinton replied, “As you know, hearing nice things about your children is as good as it gets.”
In July 2013, the Commerce Department began investigating complaints that Ukraine — and by extension Mr. Pinchuk’s company, Interpipe — and eight other countries had illegally dumped a type of steel tube on the American market at artificially low prices.
A representative for Mr. Pinchuk said the investigation had nothing to do with the State Department, had started after Mrs. Clinton’s tenure and been suspended in July 2014. He added that at least 100 other people had attended the dinner party at Mrs. Clinton’s house and that she and Mr. Pinchuk had spoken briefly about democracy in Ukraine.
A deal involving the sale of American uranium holdings to a Russian state-owned enterprise was another example of the foundation intersecting with Mrs. Clinton’s official role in the Obama administration. Her State Department was among the agencies that signed off on the deal, which involved major Clinton charitable backers from Canada.
There was no evidence that Mrs. Clinton had exerted influence over the deal, but the timing of the transaction and the donations raised questions about whether the donors had received favorable handling.
Even if Mr. Clinton steps down, there could be remaining complications about a potential president’s name being affixed to an international foundation. And Chelsea Clinton, who is its vice chairwoman, would continue her leadership role.
“It is very difficult to see how the organization called the Clinton Foundation can continue to exist during a Clinton presidency without that posing all sorts of consequences,” said John Wonderlich, the interim executive director of the Sunlight Foundation, a government watchdog group in Washington. “What they announced only addresses the most egregious potential conflicts."
Considering the scale and scope of the foundation, Mr. Wonderlich said it was easy to “name a hundred different types of conflicts.”