The three were arrested on Wednesday night when members of the Chicago police department battered their way into an apartment in the Bridgeport area of the city.
According to court documents released on Saturday, the three men considered targeting Barack Obama's re-election headquarters and the home of Chicago mayor Rahm Emanuel.
The Chicago police department said the men, described as self-proclaimed anarchists and members of the "Black Bloc" movement that has disrupted international gatherings in the past, were arrested on Wednesday and charged on Friday with conspiracy to commit terrorism, providing material support for terrorism and possession of an explosive incendiary device.
The three men charged were listed as Brian Church, 22, of Fort Lauderdale, Florida, Jared Chase, 27, of Keene, New Hampshire, and Brent Betterly, 24, from Massachusetts.
At a hearing on Saturday bail was set at $1.5m for each of the three. Their next court appearance is on Tuesday.
Supporters of the three men disputed the charges, saying the men had come to protest at the Nato summit peacefully and that the police had confused beer-making equipment with explosives.
A lawyer for the three, Michael Deutsch, said undercover police officers had entrapped them by infiltrating the group and encouraging the bomb-making effort. The Chicago police department declined to comment on the tactics employed in the case.
The Cook County state attorney's office said the three men had other weapons including a mortar, knives and a hunting bow. It said they considered attacking police stations and cars in Chicago to disrupt police operations for the two-day Nato summit that begins on Sunday.
"Some of the proposed targets included campaign headquarters of US President Barack Obama, the personal residence of Chicago mayor Rahm Emanuel and certain downtown financial institutions," the court papers said.
On Saturday several hundred activists protested outside Emanuel's home. The event was peaceful.
"The men had been making Molotov cocktails out of empty beer bottles filled with gasoline and fitted with cut bandanas for fuses," Cook County state attorney Anita Alvarez told a news conference after the bond hearing.
"It is pretty clear from the evidence they were making the bombs," Alvarez said. "There was a lot of discussion about making these Molotov cocktails and what they were going to do with them."
The charges were the state's first for violation of Illinois anti-terrorism statutes, she said.
"When it became evident there was an overt act in this conspiracy, we had to act," Chicago police superintendent Garry McCarthy said, adding the investigation that began in early May was continuing. "We did not want to take this case down as quickly as we did but we had to because of the imminent threat."
Deutsch, the attorney representing the suspects, said at the hearing that police had planted weapons at the scene of the arrests. "This is a way to stir up prejudice against a people who are exercising their First Amendment rights," Deutsch said. "There were undercover police officers that ingratiated themselves with people who come from out of town."
In a case earlier this month five self-described anarchists were charged with plotting to blow up a bridge near Cleveland after planting fake explosives underneath that federal agents had sold them.
Natalie Wahlberg, a member of the Occupy Chicago movement protesting against income inequality, said: "The charges are utterly ridiculous. CPD [Chicago police department] doesn't know the difference between home beer-making supplies and Molotov cocktails."