Earlier, Clinton had also held bilateral talks with Rangeen Dadfar Spanta, the Afghan foreign minister.
The talks come as Al Jazeera learnt that secret talks to include the Taliban in Afghanistan's political process, including Western officials, were under way.
Earlier this week the Spanta and Shah Mehmood Qureshi, the Pakistani foreign minister, had both hailed improved relations between the two states, ties which had been previously marked by rows over cross-border attacks by fighters.
Spanta said he "found a very, very positive response" to Kabul's ideas for regaining the initiative in its seven-year conflict with the Taliban and al-Qaeda.
In a speech to the Centre for American Progress policy group, however, Spanta said: "My thesis is that the main threat centre of instability in the war is not Iraq; it is not Afghanistan. It is much more Pakistan.
"If Pakistan becomes failed state, this is a serious threat for you, for us and the entire region," he said of Afghanistan's nuclear-armed neighbour, where a civilian government is dealing with continuing attacks from fighters and a severe economic crisis.
Spanta also cited the appointment of veteran diplomat Richard Holbrooke as special US envoy to the region as recognition of the need for a broader approach to the conflict.
Barack Obama, the US president, last week decided to send an additional 17,000 troops to Afghanistan, bringing the number of US troops stationed there to 55,000 by this summer.
"Afghanistan's wish is to deploy these troops in the main problem centre in some provinces in the south of Afghanistan and also for the control of cross-border activities," Spanta said.