Hamid Karzai, the Afghan president, has extended his stay in Pakistan for another day at the request of the Pakistan prime minister, Nawaz Sharif.
The decision will enable the two leaders to discuss common issues further in the context of bilateral and regional levels, Pakistani Foreign Ministry said in statement on Tuesday.
The statement indicated that Sharif will hold a new round of talks with Karzai later in the day.
On the first day of his visit, Karzai urged Pakistan to help his country defeat fighters who he said were bent on destabilising both countries.
Sharif took office in early June after winning elections in May.
Karzai said the two countries should launch a joint campaign against "the menace of terrorism" afflicting both nations and thanked Sharif for inviting him.
For his part, Sharif said constructive dialogue was essential for improving ties between the neighbours.
The two leaders have agreed to expand trade, with Pakistan offering to help with the widening of the road connecting Torkham to Jalalabad across the border.
Pakistan also offered to construct rail links from Torkham to Jalalabad and from Chaman to Spin Boldak.
Al Jazeera's Kamal Hyder, reporting from Islamabad, said while there was progress, there were serious differences between both sides.
Karzai's visit comes after a failed attempt in June to start peace talks with the Taliban in the Qatari capital of Doha.
|From the perspective of one neighbourhood in Herat
The group has refused to negotiate with Karzai's government so far, accusing it of being a puppet of the US.
Karzai's government sees Taliban safe havens in Pakistan, which has strong ties to the group, as the main reason for increased violence across Afghanistan.
Some elements of Pakistan's intelligence service have long been accused of supporting the Afghan Taliban and giving its fighters refuge on Pakistani territory, a claim denied strongly by Pakistan.
Relations between Karzai and the Pakistan President Asif Ali Zardari had appeared to improve at a summit hosted by Britain in February, but have since being affected badly due to a series of public disputes
Last month, Karim Khorram, Karzai's chief of staff, claimed that the opening of the Doha office of the Taliban was part of a conspiracy to break up Afghanistan, coordinated by either Pakistan or the US.