The US delegation is expected to press Pakistan to escalate its war against armed groups in the country's northwest - particularly the so-called "Haqqani network" - supposedly the deadliest group operating in Afghanistan whose fighters often take sanctuary in Pakistan.
Clinton will also likely press Pakistan on its role in "reconciliation" talks between anti-government fighters and the Afghan government. Some US officials suspect that Pakistan will encourage fighters with links to al-Qaeda to join the government.
"For the United States, it is key that the Afghan government, and those Taliban elements who may join it, have no links to al-Qaeda, and that Afghanistan does not again become a base for al-Qaeda," Teresita Schaffer, an analyst at the US-based Center for Strategic and International Studies, said.
The Pakistani government, meanwhile, will have several requests of its own. The US pledged billions of dollars in development aid for Pakistan last year, but the two governments are still arguing over how to disburse that aid.
Pakistan's army also hopes to secure additional military assistance from the United States.
Clinton will then travel to Kabul for an international donors' conference on Tuesday.
The Afghan government will present a long-term development strategy to dozens of prospective donors, most of whom are expected to pledge additional aid for Afghanistan. The government is also seeking more control over how international aid is spent.
This will be the ninth international conference on Afghanistan since the war began in 2001.
It will also be the largest international conference in Kabul since the 1970s. Security has already been raised across the Afghan capital, and Nato officials said on Saturday that they had foiled a plot to attack the conference.