ISLAMABAD — A week of terror strikes across Pakistan, capped by a stunning assault on army headquarters, show the Taliban have rebounded and appear determined to shake the nation’s resolve as the military plans for an offensive against the group’s stronghold on the Afghan border.

The 22-hour attack on Pakistan’s “Pentagon” in the city of Rawalpindi, which ended with 20 dead Sunday, was the third terror attack in a week to shake this nuclear-armed nation. It demonstrated the militants’ renewed strength since their leader was killed by a U.S. missile strike in August and military operations against their bases.

The U.S. has long pushed Islamabad to take more action against Taliban and al-Qaida militants, who are also blamed for attacks on U.S. and NATO troops in Afghanistan, and the army carried out a successful campaign against the militants in the Swat Valley in the spring.

But the army had been unwilling to go all out in the lawless tribal areas along the border that serve as the Taliban’s main refuge. Three offensives into South Waziristan since 2001 ended in failure and the government signed peace deals with the militants.

On the heels of the Swat victory, the military launched a campaign of airstrikes on the militants in Waziristan and in recent weeks officials said they were preparing a full offensive there.

That was before the embarrassing attack on army headquarters bolstered militants’ assertions they are ready to take on the military, and threatened to deflate the army’s newfound popularity.

In the wake of the siege in Rawalpindi, the government said it would not be deterred. The military launched two airstrikes Sunday evening on suspected militant targets in South Waziristan, killing at least five insurgents and ending a five-day lull in attacks there, intelligence officials said.

“We are going to attack the terrorists, the miscreants over there who are disturbing the state and damaging the peace,” Information Minister Qamar Zaman Kaira said. “Wherever they will be, we will follow them. We will pursue them. We will take them to task.”

In London, U.S. Secretary of State Hillary Rodham Clinton said the insurgents are “increasingly threatening the authority of the state, but we see no evidence they are going to take over the state.” She and British Foreign Minister David Miliband said there was no sign Pakistan’s nuclear arsenal was at risk.

Available information suggests that Pakistan’s secret nuclear sites are protected by crack troops and multiple physical barriers.

“It’s not thought likely that the Taliban are suddenly going to storm in and gain control of the nuclear facilities,” said Gareth Price, head of the Asia program at London think tank Chatham House.

Security at army headquarters did not prevent a team of 10 gunmen in fatigues from launching a frontal assault on the very core of the country’s most powerful institution Saturday morning, setting off a gunbattle and hostage drama that ended a day later after a commando raid.

The violence killed 20, including three hostages and nine militants, while 42 hostages were freed, the military said. Many of them had been held in a single room by a militant wearing a suicide vest, who was shot by commandos before he could detonate his explosives, the army said.

The military said it captured the militant’s ringleader, who was known as Aqeel or “Dr. Usman.” Army spokesman Maj. Gen. Athar Abbas said the militant’s nickname derived from the time he spent as a guard at an army nursing school before he joined the insurgents.

The name matched that of a militant suspected of orchestrating an attack in Lahore earlier this year on Sri Lanka’s visiting cricket team. Hakimullah Mehsud, the new leader of the Taliban, had claimed responsibility for that attack.

A police intelligence report from July obtained by The Associated Press on Saturday warned that members of the Taliban along with the Punjab-based Jaish-e-Mohammed were planning to attack army headquarters after disguising themselves as soldiers. The report was given to the AP by an official in Punjab’s home affairs ministry.

Officials have warned that Taliban fighters close to the border, Punjabi militants spread out across the country and foreign al-Qaida operatives were increasingly joining forces, dramatically increasing the dangers to Pakistan.

The weekend strike was a stunning finale to a week of attacks that highlighted the militants’ ability to strike a range of targets in different cities, seemingly at will.