Afghan President Hamid Karzai is due to meet Pakistani Prime Minister Nawaz Sharif in Islamabad for talks on restarting a peace process with the Taliban.
The BBC’s Karen Allen in Kabul says Mr Karzai will be pressing Mr Sharif to release senior Taliban prisoners.
The insurgents refuse to talk with Mr Karzai, dismissing him as a US puppet.
Afghanistan also believes Taliban safe havens in Pakistan are the main cause of increased violence in the country.
Elements of Pakistan’s intelligence service have long been accused of backing the Afghan Taliban and giving them refuge on Pakistani soil – something Islamabad strongly denies.
It will be President Karzai’s first meeting with Mr Sharif, who took office after winning elections in June.
“The first item with Pakistan will be the peace negotiations,” Mr Karzai told a news conference before leaving Kabul.
He praised Mr Sharif for having “all the right intentions for stability and peace”, but conceded that previous visits to Pakistan had not succeeded in improving security in Afghanistan.
“I’m hopeful, but not sure, I will only go with hopes, and wish they materialise,” he said.
Top of Mr Karzai’s demands are the release of high-profile Taliban prisoners held in Pakistan in the hope that this will help jump-start direct talks with insurgents, our correspondent says.
Both leaders know that economic fortunes on either side of the border depend on more stability, she adds.
Meanwhile Pakistan will be looking for more trading opportunities and strategic supply routes through Afghanistan.
Mr Karzai was said to be furious when the Taliban opened a liaison office in Qatar in June. He insists that his government should take a central role in any peace talks.