But President Zardari, during his meeting with Ms Rice, repeated an earlier promise to help investigate the attacks, his office said.
"The government will not only assist in investigation but also take strong action against any Pakistani elements found involved in the attack," he is quoted in an official statement as saying.
"Pakistan is determined to ensure that its territory is not used for any act of terrorism," he added.
Meanwhile, a Pakistani group has denied any connection with the banned militant group Lashkar-e-Toiba, which is suspected of being behind the Mumbai attacks.
A spokesman for Jama'at ud Dawa, Abdullah Muntazir, suggested homegrown Indian militants were involved instead. "I do not believe the attacks in Mumbai could have been carried out by Muslims," he told reporters.
Ms Rice described her talks with Mr Zardari, Prime Minister Syed Yusuf Raza Gillani and the country's army chief as "quite satisfactory".
Condoleezza Rice on the 'sophisticated' attack in Mumbai
"I have found a government that is focused on the threat and understands its responsibilities to respond to terrorism and extremism," she told a news conference.
She said Pakistan would investigate any links with Mumbai, "because the Pakistani government... does not in any way want to be associated with terrorist elements and is indeed fighting to root them out wherever they find them."
Before arriving in Islamabad, she told reporters Pakistan must take a "tough line" on terrorism.
Ms Rice travelled to Pakistan from India where she called on both countries to show moderation in their response to the Mumbai attacks.
While Pakistan needed "a robust response", India should not take actions that would provoke "unintended consequences", she said.
Jihadi organisation based in Pakistan
Formed towards the end of the Afghan war against the Soviets
Blamed for hundreds of attacks in the region since 1990
US Joint Chiefs of Staff Chairman Mike Mullen has been pushing the same message, in meetings with defence officials in Pakistan on Wednesday and India on Thursday.
The pressure from India to take action against militants it claims were involved in the Mumbai attacks puts Pakistan's government in a difficult position, the BBC's diplomatic correspondent Jonathan Marcus says.
The authorities in Islamabad may doubt the capacity of their own security forces to carry out such orders, he says.
And, by acceding to Indian pressure, Pakistan might risk deeper civil strife at home. Overt Indian military action might provoke a new stand-off that would do nothing for Pakistan's stability, which remains an ever shakier corner-stone of US and western efforts to win the war in Afghanistan, our correspondent adds.
Last week's attacks at multiple locations in India's financial capital stunned the country, with many describing it as India's 9/11.
Three major airports in India are on heightened alert after a threat of more possible attacks by the Deccan Mujahideen, the previously unknown militant group who claimed responsibility for last week's Mumbai attacks.
Meanwhile, the resignation of Vilasrao Deshmukh, chief minister of the state of Maharashtra where Mumbai is located, was accepted by the governing Congress Party on Thursday.
His was one of a number of resignations in the wake of the attacks amid growing fury over the government's handling of the crisis.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.