Mr. Soros, a Holocaust survivor originally from Hungary, said in a telephone interview this week that he was “deeply troubled” by hundreds of reports of possible hate crimes since the election — including many Nazi swastikas spray-painted on cars and buildings.
“We must do something to push back against what’s happening here,” Mr. Soros said, blaming what he termed the “dark forces that have been awakened” by the election.
Groups that oppose Mr. Trump’s policies have reported record donations since the election, among them the American Civil Liberties Union, the Sierra Club and Planned Parenthood.
Mr. Soros, a billionaire investor, is one of the biggest donors to liberal and Democratic causes in modern times, making him a frequent target of conservatives who criticize what they say is his outsize financial influence in politics.
He said his $10 million commitment for the hate crime initiative, the single biggest gift of its kind to emerge since the election, was not intended as a political statement on Mr. Trump. But he did say he believed campaign statements from Mr. Trump and his supporters — including disparaging remarks about Muslims, Mexicans, women and others — were “directly responsible” for the recent outbreak of episodes.
“Certainly it got inflamed as a result of the campaign, and it broke out really afterwards,” he said.
His nonprofit group, the Open Society Foundations, plans to spend at least $5 million in coming weeks to fund grants of as much as $150,000 to community groups and civil rights organizations to develop plans for combating the recent spate of hate crimes and to work with victims.
The group said additional money would go toward national efforts to improve tracking of hate crimes — an effort that law enforcement officials acknowledge is incomplete. The F.B.I. reported last week that there was an increase of nearly 67 percent last year in hate crimes against Muslim Americans — and an increase of 6 percent against all groups.
Between the election and Friday, the Southern Poverty Law Center received more than 700 reports of harassment and possible hate crimes, it said — with the majority coming in the days immediately after the Nov. 8 election. Immigrants were the most frequent targets, the center said, but blacks, gays, Muslims and other minorities also reported being victimized in schools, streets and houses of worship. The episodes have included both verbal harassment and physical attacks.
The group said it had also received 27 complaints of episodes targeting supporters of Mr. Trump.
This week, Gov. Andrew M. Cuomo, Democrat of New York, announced the creation of a new state police unit and other steps to combat what he called the “explosion of hate crimes in our state.”
In an interview with CBS News’s “60 Minutes” that aired days after the election, Mr. Trump was asked about reports that some of his supporters had harassed or attacked minorities after his victory. “I am so saddened to hear that,” he said. “And I say, ‘Stop it.’ If it helps, I will say this, and I will say right to the cameras: ‘Stop it.’”
He has also faced criticism over the political support he has received from so-called alt-right groups, including white supremacists who gave “Hail victory” salutes at a Washington convention last weekend.
“I disavow and condemn them,” Mr. Trump told The New York Times on Tuesday.
Correction: November 22, 2016 Because of an editing error, an earlier version of this article misstated when “60 Minutes” aired an interview with President-elect Donald J. Trump. It was Nov. 13, not Nov. 20.