Stein sued Pennsylvania election officials in federal court, demanding a statewide recount. Michigan workers began a Stein-requested recount after a federal judge there ordered one without delay. In Wisconsin, a recount that Stein requested continued into a second week.
Even if all three recounts are completed, they are extremely unlikely to change the outcome of the November 8 election in which the three states, which had voted Democratic in recent presidential elections, helped seal a victory for Trump, a Republican.
On Sunday, Trump proclaimed Stein's effort a failure and questioned her motives, saying on Twitter: "Just a Stein scam to raise money!"
At a news conference on Monday across the street from Trump Tower in Manhattan, Stein said every dollar she raised for the recount was going to an account for that purpose. She has raised $7.2 million towards a $9.5 million goal, according to her website.
"We urge Donald Trump to look at the facts, not to make up the facts," Stein said.
Stein said her recount push in the three "Rust Belt" states was not meant to change the election's result but to focus attention on concerns about the integrity of voting systems in the three states.
Trump and his supporters have fought to end the recounts by filing lawsuits.
"We are here to assure Donald Trump that there is nothing to be afraid of," Stein said. "If you believe in democracy, if you believe in the credibility of your victory, put down your arms, end your bureaucratic obstruction."
Some voting machines in Pennsylvania lack a paper trail, making them vulnerable to hacking or other problems, she said.
Trump Tower protest
A few Trump allies protested Stein's appearance with her supporters at Trump Tower, where Trump's offices and apartment home are located.
"I think the people out here today don't believe in democracy," said Jim MacDonald, a 67-year-old actuary from the borough of Queens. He held a sign that read: "Dr Jill is a quack," and said he voted for Trump.
"He's their president whether they like it or not," MacDonald said.
Stein took about 1% of the popular vote, far behind Trump and Democrat Hillary Clinton.
Although Clinton won the national popular vote, she lost to Trump in the Electoral College, the 538-person body chosen state-by-state that actually selects the president.
Trump won a projected 306 electoral votes and is scheduled to be sworn in on January 20. Stein won no Electoral College votes.
December 13 deadline
Federal law requires states to resolve disputes over the appointment of electors by December 13, adding pressure on Michigan, Pennsylvania and Wisconsin to wrap up any recounts.
In Wisconsin, the recount has produced only minor shifts because of human error, state officials said on Monday. In one county, Clinton gained 13 votes that were not counted on Election Day because voters used non-standard pens to mark their ballots.
An initial request by Stein for a recount in Pennsylvania failed on Saturday after a state judge ordered her campaign to post a $1 million bond. A federal lawsuit was her next best option, she said.
A spokeswoman for Pennsylvania election officials said they would not comment on pending litigation.
In Michigan, the state said on Monday that a recount of presidential ballots had begun after an order from a federal judge directing officials to complete the process by December 13.
US District Judge Mark Goldsmith issued the written order early on Monday after a Sunday night hearing in federal court in the Eastern District of Michigan.
Goldsmith ordered that, once started, the recount "must continue until further order of this court." The state had planned to wait until Wednesday to begin the recount.
In his ruling, Goldsmith wrote that "budgetary concerns are not sufficiently significant to risk the disenfranchisement of Michigan's nearly 5 million voters."
The Michigan Republican Party filed court papers to appeal Goldsmith's ruling.
Michigan Attorney General Bill Schuette, a Republican, sued on Friday to halt the requested recount in the state, which Trump won by about 10,700 votes. The Michigan Court of Appeals has scheduled a hearing on Schuette's suit for Tuesday afternoon.
Although the Clinton campaign did not initiate the recount effort, it says it is participating to make sure the process is fair to all sides.