At one point they tried to push their way into the palace but the army inside resisted, she said.
The protesters were calling for the reinstatement of Zelaya, who was taken by soldiers from his home in his pyjamas on Sunday and sent to Costa Rica after he tried to carry out a referendum to extend his term in office.
Micheletti, from the same Liberal party as Zelaya, promised to govern with "transparency and honesty" and "work tirelessly to restore peace and tranquillity that we have lost".
He said Zelaya was not ousted through a coup but by a legal process.
"I came to the presidency not by a coup d'etat but by a completely legal process as set out in our laws," Micheletti said after being sworn in by congress.
"What we have done here is an act of democracy, because our army has complied with the order of the court, prosecutors and judges," Micheletti said, winning loud applause from legislators.
|Zelaya was elected for a non-renewable
four-year term in 2006 [File: AFP]
But Zelaya said he had been a "victim of kidnapping" when Honduran soldiers raided his home earlier in the day.
"They came to my house in the early hours of the morning and firing guns, they broke the doors with bayonets and threatened to shoot me," Zelaya told Venezuela's Telesur television station after being taken by troops to Costa Rica.
Calling for "peaceful resistance", he said he did not "think that the whole army supported this interruption of the democratic system by capturing a president elected by the people".
Zelaya appeared to have little support in Honduras among the military, parliament or the judiciary.
Colin Harding, an expert in Latin American politics, told Al Jazeera that Zelaya had apparently overestimated his own power in pushing for the referendum.
"He has no support within his own party, he is opposed by congress, he is opposed by the judiciary and the military, who are not the power they used to be but have lined up against Zelaya ostensibly in defence of legality," he said.
The supreme court said it had ordered his removal in order to protect law and order in the nation of about seven million people.
"Today's events originate from a court order by a competent judge," it said, adding that the armed forces "acted to defend the state of law".
Congress said it had voted unanimously to remove Zelaya from office for his "apparent misconduct" and for "repeated violations of the constitution and the law and disregard of orders and judgments of the institutions".
Zelaya, who was elected in November 2005 to a non-renewable four-year term, had sought to revise the constitution through a referendum to allow him to run again in the next elections.
The supreme court had ruled such a referendum illegal, but Zelaya had tried to press ahead with a vote on Sunday regardless, triggering the coup.
Micheletti is set to stay in office until January 27 next year, when a new president elected in elections planned for November is due to take over.
The UN General Assembly announced it would hold an emergency session on Monday to discuss the unrest in Honduras at the request of Honduran ambassador to the UN, Jorge Reina Idiaquez.