KABUL, Afghanistan — In a series of audacious strikes on the eve of the new U.S. special envoy’s scheduled arrival in Afghanistan, Taliban gunmen and suicide bombers on Wednesday staged synchronized raids on three government buildings in the heart of Kabul, killing at least 20 people and injuring scores of others.

Prolonged bursts of gunfire rattled through city streets. Some terrified government workers jumped out second-story windows to escape. At the Justice Ministry, the minister was trapped for a time in his office as fighting raged in the corridors.

The attacks, which came days after the Afghan government said it had cracked a suicide-bombing ring active in the capital for nearly two years, underscored militants’ continuing ability to penetrate even extremely heavy security surrounding official installations.

The Obama administration, with NATO allies, is struggling to put together a new strategy for Afghanistan, where Islamic insurgents are gaining ground and many Afghans are disillusioned by the pervasive insecurity that plagues their daily lives. On Tuesday, the White House said it plans to complete an overhaul of policy on Afghanistan and Pakistan by April; American military commanders, meanwhile, have said they could send an additional 30,000 troops to the troubled country this year, nearly doubling the U.S. contingent.

Seven years after the U.S.-led invasion that toppled the Taliban, Kabul’s inner districts are a tangle of blast walls and security checkpoints. But insurgents apparently managed to send a squad of at least eight assailants, clad in suicide vests and toting assault rifles, into some of the city’s most secure areas to carry out Wednesday’s attacks, officials acknowledged.

Some of the fighting took place a short distance from the presidential palace, where Richard Holbrooke, the new American special envoy to the region, is likely to visit. Holbrooke’s schedule was not announced for security reasons, but Afghan officials had said he was expected in Kabul today.

In recent days, Holbrooke has been in Pakistan, where he traveled by helicopter Wednesday to the lawless tribal areas to see the positions of Pakistani troops battling the Taliban on their side of the Afghan-Pakistan border.

In Afghanistan, securing the provinces adjoining Kabul has become a high priority for Western military commanders. More than 3,000 U.S. troops have been deployed in the last month in Logar and Wardak provinces, just to the south of the capital, after militants established a foothold there, cutting off traffic on the country’s main highway.

The justice minister, H.E. Sarwar Danish, said during the siege that the attackers on his building were armed with grenades and assault rifles. The fighting continued for more than an hour before the ministry was secured.

A Taliban spokesman, Zabiullah Mujahid, said the attacks were meant to avenge the treatment of captured insurgents allegedly tortured in prison.

After hours of contradictory reports about the death toll, Afghanistan’s interior minister, Mohamad Hanif Atmar, said 20 people had been killed and 57 hurt, some of them critically. The dead included nine members of the Afghan security forces and 10 civilian workers at the Justice Ministry, Atmar said.

Earlier, other officials said eight assailants were killed, although it was not clear where or how they died.

Installations targeted in the attacks also included the Education Ministry and an office of the prisons department. The use of multiple suicide bombers is not a new tactic for the Taliban, but in a departure from past practice, the assailants apparently tried to kill as many victims as possible with gunfire before setting off suicide blasts. At least three succeeded in blowing themselves up after the initial assault with grenades and gunfire, according to initial reports.