In an address from the presidential palace, Nicolas Maduro said the helicopter had flown over the Supreme Court and also the justice and interior ministries.
Officials quoted by Reuters said four grenades were dropped on the court and 15 shots had been fired at the interior ministry.
No injuries were reported but President Maduro said “a social event” had been taking place at the Supreme Court and the attack could have caused “dozens of deaths”. One of the grenades failed to detonate, he added.
Nicolas Maduro has placed the military on alert.
“I have activated the entire armed forces to defend the peace,” he said.
“Sooner or later, we are going to capture that helicopter and those who carried out this terror attack.”
The police officer identified himself as Oscar Pérez in video statements posted on the social media platform Instagram.
Appearing in military fatigues and flanked by armed, masked men in uniform, he appealed to Venezuelans to oppose “tyranny”.
Venezuela’s Supreme Court has ruled that the delay of President Hugo Chavez’s inauguration for a new term in office is legal.
Earlier, the National Assembly voted to give Hugo Chavez as much time as he needed to recover from cancer surgery.
The opposition argues that Hugo Chavez’s current mandate expires on 10 January, the day he is due to be sworn in.
Hugo Chavez is in hospital in Cuba and has suffered complications caused by a lung infection.
Supreme Court President Luisa Estella Morales said it would be “absurd” to consider Hugo Chavez’s treatment in Cuba as an unauthorised absence.
She said that the oath of office could be taken at a later date, as the constitution states, and Hugo Chavez’s re-election had guaranteed “continuity” in government.
In a televised statement, Estella Morales read out the unanimous decision of the panel of seven magistrates who handle constitutional issues before the court.
She said there was a clear distinction between the act of taking the oath and the beginning of a new mandate.
Venezuela’s Supreme Court has ruled that the delay of President Hugo Chavez’s inauguration for a new term in office is legal
The Supreme Court considered the swearing-in an important formality, but not indispensable for the start of the new presidential term, she said.
According to the opposition, Hugo Chavez should be declared temporarily incapacitated with the current Speaker of the National Assembly, Diosdado Cabello, not Vice-President Nicolas Maduro, taking over as caretaker leader.
They argue that Nicolas Maduro, who was appointed by Hugo Chavez not elected, will cease to be vice-president on 10 January.
But Estella Morales said that “the executive power made up of the president, vice-president, ministers and other organs, as well as administration officials, will continue to carry out their functions under the principle of administrative continuity”.
She said that the swearing-in ceremony would no doubt happen.
“But at this moment, we can’t say when, how, or where he [the president] will be sworn in,” Estella Morales said.
President Hugo Chavez, who has been in power since 1999 and was re-elected in October for a fourth term, has not been seen or heard in public for almost a month.
Diosdado Cabello has called on Hugo Chavez supporters to take to the streets of Caracas on Thursday to show support for him.
He said several foreign leaders had agreed to be at the Miraflores Presidential Palace on inauguration day.