President Gen. Pervez Musharraf made his comments at a meeting with Clinton, who called on him along with Senator Evan Bayh and Congressman John McHugh in the eastern city of Lahore late Sunday.
Pakistan is a key ally of the United States in its war on terror.
The visit by Clinton - the wife of the former U.S. president who is considering a run for the job - came weeks after Musharraf's government announced a plan to plant land mines and build a fence along parts of its frontier with Afghanistan to stop Taliban and al-Qaida guerrillas from crossing over.
The Afghan government has opposed the plan, saying it would separate families instead of preventing cross-border terrorism.
At the meeting with Clinton, Musharraf said a "peaceful and stable Afghanistan was in Pakistan's vital interest," according to a Foreign Ministry statement.
It said Musharraf asserted that security along the shared border was a joint responsibility and that both sides should make an effort to ensure stability in the region, the AP reports.
Musharraf also "underlined the importance of the strategic relationship between Pakistan and the United States and expressed satisfaction at the deepening of cooperation in diverse fields," it said.
According to the statement, Musharraf also "affirmed Pakistan's firm resolve to fight extremism and terrorism," and in this context, he "highlighted holistic approach being followed by Pakistan."
Clinton, a senator from New York, praised Pakistan's role in the fight against terrorism, the AP says.
Pakistan was once a main ally of the Taliban. But it switched sides after a U.S.-led coalition force invaded Afghanistan to oust the Taliban after the Sept. 11, 2001, terror attacks in the United States.
Since then, Pakistan has deployed about 80,000 troops in tribal areas near Afghanistan to flush out foreign militants and their local supporters.