Maduro, sworn in as president of the South American country Friday, said in his speech he wanted his government to be open to "all Venezuelans," the BBC reported.
"I want to extend the hand so we can build an inclusive nation for everybody," he told the audience.
During his speech, a man grabbed the microphone but was removed by security forces, witnesses said. Maduro later criticized security.
"I could have been shot here," he told the audience, later saying he would try to speak to the man.
Officials said they didn't know why the man rushed Maduro, the British broadcaster said.
Maduro succeeds Hugo Chavez who died of cancer in March after ruling for 14 years. He beat opposition leader Henrique Capriles in Sunday's election.
Election officials said they would audit the vote after Capriles claimed there were irregularities. He said he would accept the electoral audit.
In his speech, Maduro promised a "revolution within the revolution."
"I'm willing to even talk to the devil ... if necessary to stop his hatred against me, against the people, to stop his intolerance," he said.