When President Hamid Karzai left for Washington this week, some Afghans wondered what he would bring back. Their leader had a long list of demands, but he would be meeting with an American president whose top priority was a U.S. military withdrawal.

The meeting between the two leaders at the White House on Friday appears to have yielded progress on at least two of the issues on Karzai’s list: a U.S. pullout from Afghan villages and a full handover of the country’s military detention center at Bagram.

But neither Obama nor Karzai spoke concretely about the size of the U.S. presence here after 2014, with Karzai saying, “Numbers are not going to make a difference to the situation in Afghanistan.”

In Kabul, though, there is still great interest in that question, and some voiced disappointment Saturday that neither president offered clarity on an issue that weighs heavily on the minds of many Afghans.

“We wanted to hear from our president key questions about Afghanistan beyond 2014, like: What will be the role of the U.S. militarily and politically? What is the Afghan government’s demand from the U.S.?” said Fauzia Koofi, a lawmaker and women’s rights activist. “Those issues were not mentioned by President Karzai.”

Although both leaders spoke of their interest in a long-term security partnership, Karzai expressed uncertainty about whether diplomatic immunity would be provided to U.S. troops beyond 2014, a prerequisite for an enduring troop presence, according to Obama. For Afghans worried about a dramatic U.S. withdrawal, the prospect that the Americans won’t offer Karzai the concessions he needs to grant that immunity prompted concerns.

“Karzai thought that through pressure on the issue of legal immunity, we could gain concessions, but there is no sign that those concessions will be given to Afghanistan,” said Waheed Mozhdah, a longtime Afghan analyst.

“There was no special achievement for Karzai in this trip, but it added to the concerns that American forces may not keep troops after 2014,” Mozhdah added.

At a joint news conference Friday, Obama announced that the transition to Afghan-led security would be accelerated, with Afghan troops and police taking control of all operations in the spring. Remaining U.S. troops will serve a supporting role, he said.

News of the acceleration drew a mixed response from top Afghan commanders confident in their troops’ abilities but concerned about a lack of equipment.

“We have sufficient arms and enough physical strength and manpower on the ground that will allow us to defeat the insurgents,” said Gen. Abdul Hamid, the top Afghan commander in the southern province of Kandahar and the leader of the army’s 205th Corps. “But our army is not complete in terms of equipment. We lack artillery, rockets and an air force.”

Like many other parts of the country, Kandahar has begun the formal process of transition to Afghan-led security. But Afghan forces there still rely on U.S. troops for air support and logistical assistance. Many within the Afghan security forces and political establishment are eager to know how those roles, along with U.S. political involvement, will change after 2014, particularly now that the White House has acknowledged the possibility that no troops will remain in the country after next year.

“We wanted a clearer message from Obama that the U.S. will continue to support democracy in Afghanistan,” Koofi said. “It’s the only alternative to Talibanization.”