As Army Chief, General Kayani is the man behind the curtain of Pakistani power, controlling an Army that has ruled for much of Pakistan's 61 years. Without Kayani's support, Mr. Zardari can do little against Lashkar-e-Taiba, the group tied to the Mumbai (formerly Bombay) attacks.
One year into the job, Kayani has been a reformer – clipping the Army's interference in politics and mounting offensives against militants in Pakistan's tribal areas.
But today's crisis poses unique challenges: His Army is stretched and in no mood to do its archrival's bidding.
As India applies more pressure, the days ahead will test Zardari, Kayani, and Pakistan's often-inverted chain of command.
"We are starting to see a greater cooperation between the government and the Army," says Ahmed Rashid, a political analyst in Lahore. But, he adds, it is a "fluid situation that is changing day to day."
Thursday, as India announced plans to restructure its counterterrorism forces it also had strong words for Pakistan. In an address to Parliament, Foreign Minister Pranab Mukherjee said Pakistan's arrest this week of several Lashkar-e-Taiba leaders was not enough, demanding that Pakistan turn over 40 people it lists as terrorists.
He also hinted at India's suspicions that the Army, and not the civilian government, is running Pakistan. Though he pleaded with Pakistan to "please act," he added that India had "no quarrel" with the democratic government.
There is some truth in his statement, says Mr. Rashid. "The Army is still in control of foreign policy and policy with regards to India and Afghanistan," he says. "If the Army doesn't want to do something it won't."
That was true in July, when Pakistan's civilian leaders tried to bring the nation's top intelligence agency, the Inter-Services Intelligence (ISI) directorate, under the control of the Interior Ministry. The Army denied the move. The Army has also refused to hand over control of Pakistan's nuclear arsenal.
But the dynamic is slowly changing, Rashid says. Kayani has removed some 3,000 active and retired military personnel from civilian government posts, and he deactivated the political wing of the ISI, which had long been accused of intimidating or blackmailing politicians opposed to the Army.
He continued to subordinate the military to civilian control last week by allowing the disbanding of the National Security Council, an influential panel dominated by the president and military.
Its functions will now be fulfilled by the parliamentary Defense Committee, which made the decision to arrest the Lashkar-e-Taiba leaders earlier this week, Rashid says.
Kayani's purpose is to move the Army back toward its core functions, such as war fighting, and away from political intrigue, says Shuja Nawaz, author of "Crossed Swords: Pakistan, Its Army, and the Wars Within."
"It appears that the Army is trying to retool itself and is quite happy for the civilians to make the decisions," he says. After the Musharraf years, in which Army generals got rich off real estate and construction deals, Kayani "is convinced that the military needs to return to its professional roots."
He is the product of a different mind-set, says Badar Alam of the Pakistani magazine, The Herald. Kayani served as military secretary to former Prime Minister Benazir Bhutto, Zardari's late wife, and he attended the Command and General Staff College in Fort Leavenworth, Kan.
"Kayani has a much more liberal outlook" than past Army chiefs, says Mr. Alam.
This extends to his view of militants, he adds. Kayani and his top brass are not of the generation that rose through the ranks by cultivating militant networks – such as the Taliban and Lashkar-e-Taiba – to strike at Indian interests throughout the region.
"Their relationship with militants is not as strong," Alam says.
It is one reason he has been willing to launch the largest attack against militants in Pakistan's history. The Army says it has deployed 120,000 troops into the areas bordering Afghanistan, while the United States has begun to carry out complementary operations on the Afghan side of the border to catch militants in a vise.
In a Pentagon teleconference, Col. John Spiszer claimed the biggest success of the operation was the growing cooperation between forces.
It offers the hope that Zardari will have a free hand in dealing with Lashkar-e-Taiba, should he choose to.
On Thursday Indian Foreign Minister Mukherjee demanded it. He asked Pakistan for a "complete dismantling of the infrastructure facilities available from that side to facilitate terrorist attack [and] banning the organizations."
Pakistan has begun by banning Jamaat-ud-Dawa, the charity that the United Nations designated as a front for Lashkar-e-Taiba Wednesday. The head of the charity, Hafiz Saeed – who also founded Lashkar-e-Taiba – has been put under house arrest.
Yet there appear to be limits to how far the Army is willing – or able – to go. In the hours after terrorists began their rampage in Mumbai, Pakistani Prime Minister Yousaf Raza Gilani offered to send the head of the ISI to India. He later retracted the offer, though it is not clear whether that was the result of public opinion or Army obstinacy.
More significantly, the Army feels it lacks the capacity to take on Lashkar-e-Taiba, which has its roots in Punjab, the heart of Pakistan. "Punjab would not be a small operation," says Mr. Nawaz.
With forces already deployed in the tribal areas and concern about a potential attack across the Indian border, "they can keep tabs on Lashkar-e-Taiba, but they don't want to open that front at this point," says Moeed Yusuf, a Pakistani military expert at Boston University.
"There's a desire to put the house in order one by one," starting with the tribal areas, he continues.
Besides, the Army already feels antagonized by the US, which has been firing missiles at terrorist targets in Pakistan, though there are reports of a secret deal with Pakistan allowing this.
Still, the US is a major ally and donor. India is neither. Says Nawaz: Zardari and Kayani "can't be seen to be folding to Indian demands."