An arraignment is a formal presentation of the charges.
There were no reports of pleas, but the New York Daily News said state Sen. Malcolm Smith "bolted" from a White Plains, N.Y. courtroom after he was accused in a bribery scheme.
Smith's attorney asserted his client's innocence.
"The allegations in this complaint do not tell the full story," defense lawyer Gerald Shargel, the Daily News reported.
The New York state senator and New York City councilman were arrested Tuesday, accused of trying to rig this year's New York mayoral race, officials said.
Smith, D-Queens, a contractor and real estate developer who briefly became the state Senate's first black president, and City Councilman Daniel J. Halloran III, R-Queens, were among those arrested in the corruption case that cut across political lines, The New York Times reported.
Speaking in Buffalo, N.Y., Gov. Andrew Cuomo said Smith faces very serious charges.
"I hope that [Smith] fully cooperates with the investigation and I hope that the investigation is thorough and speedy and gets to the facts," Cuomo said. "But it is very troubling," the New York Daily News reported.
"We have zero tolerance for any violation of the public integrity and the public trust."
Other political leaders arrested included GOP county-level leaders in Queens and the Bronx, as well as the mayor Spring Valley in Rockland County and her deputy, a criminal complaint indicated.
"Elected officials are called public servants because they are supposed to serve the people. Public service is not supposed to be a shortcut to self-enrichment," FBI New York Assistant Director in Charge George Venizelos said in a statement. "People in New York, in Spring Valley -- in any city or town in this country -- rightly expect their elected or appointed representatives to hold themselves to a higher standard. At the very least, public officials should obey the law."
"As alleged, these defendants did not obey the law; they broke the law and the public trust," Venizelos said. "There is a price to pay for that kind of betrayal."
The criminal complaint was unsealed Tuesday. Smith, Halloran and the others were to appear Tuesday before a U.S. magistrate judge in White Plains, N.Y.
The complaint indicated Smith agreed with a cooperating witness and an undercover FBI agent, posing as a rich real estate developer, to pay off GOP county committees leaders in New York's five boroughs to get certificates authorizing him to run for mayor as a Republican even though he was a registered Democrat.
The undercover agent and the cooperating witness acted as intermediaries between the senator and Halloran, the complaint said.
The complaint outlined the scheme borne from clandestine meetings, the Times said. The meetings were recorded by the undercover agent or the cooperating witness and primarily involved Smith or Halloran, the undercover agent and the witness.