Madonna’s speech, which was criticised on social media, led some television networks to abruptly stop their live feeds of the march.
The march drew hundreds of thousands of people in demonstrations across the U.S. to protest the election of Donald Trump as president.
“I am not a violent person,’’ the singer songwriter said on Instagram.
“I spoke in metaphor and I shared two ways of looking at things — one was to be hopeful, and one was to feel anger and outrage, which I have personally felt.’’
The 58-year-old led the crowd on Saturday in chants of, “Yes, we’re ready’’ to take on policies promoted by Trump, who alienated many women during the election campaign.
He had made comments about rivals’ attractiveness and promised to outlaw or diminish abortion rights.
Trump’s comments in a decade-old video declaring that women would allow him, as a celebrity, to kiss and grope them without their consent further outraged many women.
But Madonna preceded the chants with coarse words for critics of the march.
“To our detractors that insist that this march will never add up to anything, fuck you,’’ the pop star said.
She then repeated the expletive.
Her words drew immediate criticism on social media.
On YouTube, where the speech was posted live and in recorded formats several users called the singer “evil.’’
Others expressed outrage over her comment that she had thought about blowing up the White House. On Twitter, some users demanded that she be investigated for making terrorist threats.
Turnout for Saturday’s march was unprecedented, as organisers took credit for mobilising five million marchers worldwide.
Official crowd estimates for the Washington centerpiece of the demonstration were not available, but turnout in the nation’s capital clearly exceeded the 200,000 projected in advance by organisers.
The march filled long stretches of downtown Washington around the White House and the National Mall.