Barack Obama is to use the Nato summit to press the Afghan leader Hamid Karzai to engage with greater urgency with the Taliban about a political settlement in Afghanistan.
The US president flew to Chicago on Saturday night after 24 hours of negotiations with the leaders of the G8, dominated by the eurozone crisis but which also included talks on issues including Afghanistan.
With US allies pressing for a speedy exit from a war their countries have become weary of, Obama is to discuss with Karzai and Nato allies a timetable that will see Afghan forces taking over combat duties from the US and its allies by the middle of next year.
Almost all international forces are scheduled to be out by the end of 2014 after completion of the Afghanistan elections. Karzai will not be standing in that election.
The Obama administration had hoped Chicago would be the venue for a major announcement of a political settlement with the Taliban. But these hopes crumbled when the Taliban walked away from reconciliation talks in March.
Instead, Obama is having to focus on trying to keep the international force together until the end of 2014, with some countries already preparing to leave early, in particular France, which has said it will remove combat troops by the end of this year.
After the pullout in two years time, a Nato force will be left behind, in part to help with training.
No figure has yet been announced but US commanders in Kabul have spoken of around 15,000-20,000 personnel.
Announcements about contributions from Nato countries towards the $4.1bn needed to finance that force for 10 years are to be made at the Nato summit.
The Pakistan president Asif Ali Zardari is also in Chicago, but no bilateral meeting with Obama has yet been announced.
The US and Pakistan are engaged in negotiations about re-opening a supply route to Afghanistan which was closed after the killing of Pakistan troops in a US air strike.
Rhodes said that though no bilateral meeting is planned, Obama and Zardari would be together during a Nato session on Afghanistan and the two would have a chance to chat then.
"On the supply lines, we believe that this is going to be resolved. There have been positive steps, statements made by the Pakistanis, and we're currently negotiating the opening of the supply lines with them; we expect that to take some time. So there is still work to be done through those negotiations," Rhodes said. "We're not anticipating necessarily closing out those negotiations this weekend."
He continued: "A lot of it is happening, frankly, at the working level between our governments. We'll obviously keep you updated, but it's our sense that both sides want to get it done, it will get done. But right now, we're in a process of negotiation about how exactly that's going to happen."
Rhodes said Obama had not been briefed about the arrest of three activists alleged to have been planning to throw molotov cocktails at Obama's campaign headquarters in Chicago as well as the home of Chicago mayor Rahm Emanuel.
"We're very confident in the ability of Chicago, together with the United States government, to have a very successful event over the course of the next two days.
"If these more serious allegations are true, then I think it was effective work in making sure that they couldn't pose any additional threat to public security," Rhodes said.
