Mr Qureshi told Mr Miliband Pakistan would find the "full facts"
UK Foreign Secretary David Miliband has urged Pakistan to act more quickly against extremists in the wake of the attacks on the Indian city of Mumbai.
"The whole international community want Pakistan to go further and go faster," Mr Miliband said in Islamabad.
The Pakistani government responded by saying it would conduct an open inquiry into the attacks last year, which killed more than 170 people.
It says that it is determined to uncover the "full facts".
"I want the Pakistan government to take action because British people have been hurt... because terrorism from Pakistan is a threat to the stability of the whole region."
He said that he believed the government in Islamabad "is serious in its commitment to prosecute those associated with the Mumbai attacks. Steps have been taken".
Mr Miliband met Prime Minister Yousuf Raza Gilani, Foreign Minister Shah Mehmood Qureshi and is also due to meet President Asif Ali Zardari.
"Pakistan remains determined to uncover the full facts pertaining to the Mumbai incident," a Pakistani foreign ministry statement said.
Mr Qureshi said that information provided by India - in addition to Pakistan's own investigations - would "establish legally tenable evidence to bring the perpetrators to justice".
Relations between the South Asian neighbours have been under severe strain since November's attacks, which India has blamed on Pakistan-based militants.
On Friday, Indian Foreign Minister Pranab Mukherjee said Delhi would "never give up the demand that the perpetrators of terror acts should be extradited to India".
He said only "transparent and verifiable [investigations] in Pakistan can unveil the full conspiracy".
Mr Miliband has also spent three days in India on his visit and gave a key speech at the Taj Palace hotel - site of one of the Mumbai attacks.
The BBC's Barbara Plett in Islamabad says that so far Mr Miliband's message has been very clear.
The Taj Palace attack - Mr Miliband spoke there on Thursday
He has disagreed with Indian accusations that Pakistan's state institutions were involved in the Mumbai attacks and has not supported Indian demands for the extradition of militant suspects.
But he has said there is no doubt the attack originated in Pakistan and he has repeatedly stressed that Islamabad must bring the suspects to trial and punish them if they are found guilty.
Our correspondent says that this seems to be the consensus among other countries India has approached, seeking international backing for its demands that Pakistan take action.
Delhi has blamed Pakistan-based militant group Lashkar-e-Taiba for the attacks on India's financial capital and believes "official agencies" played a part.
Both Lashkar-e-Taiba and the Pakistani government have denied any involvement.
On Thursday, Pakistan said it had so far arrested 71 people in a crackdown on groups allegedly linked to Mumbai.
Interior ministry chief Rehman Malik said officials had also shut several schools run by a charity linked to Lashkar-e-Taiba.