Obama's visit comes amid an upsurge in fighting between the Taliban, international and Afghan forces.
Two French aid workers were kidnapped in Afghanistan on Friday, Action Against Hunger said in a statement, and a suicide bomber wounded an officer and a child when he detonated his explosives at a police checkpoint in Kandahar on Saturday.
Speaking on the plane before it landed in Afghanistan, Obama said: "We have one president at a time so I'm not gonna be travelling to negotiate anything or making promises.
"I am there to listen, but there is no doubt that my core position, which is that we need a timetable for withdrawal, not only to relieve pressure on our military but also to deal with the deteriorating situation in Afghanistan and to put more pressure on the Iraqi government, is now a position that is also held by the Iraqi government."
Obama said that it was time to respect the wishes of Iraq as a sovereign government and start withdrawing troops. A move he said, is in the strategic interests of the US.
Al Jazeera's James Bays, reporting from the capital, Kabul, said Obama's visit is attracting a lot of attention even among ordinary Afghans.
"His visit is cloaked in secrecy ... during his time here he will meet the Afghan president, Hamid Karzai, although there will be no press conference just an opportunity for the two leaders to speak and pose for photographs."
Bays said that if Obama is elected president and takes office in January 2009, then the Afghan elections will be one of his top priorities because Karzai will also be facing elections in the next year.
"Afghanistan is one of Barack Obama's top priorities ... his key note speech on foreign affairs and he spoke for much of that speech about Afghanistan.
"He said he was going to withdraw troops from Iraq in his first year in office, and he was going to send two extra combat brigades to Afghanistan, an extra $1bn each year for this country."
The senator has said that Afghanistan is the central front in the so-called "war on terror," and he is expected to call for more US action to rout the Taliban and al-Qaeda.
Obama is also expected to visit Iraq on his tour ahead of the November election. Also in a surprise visit, Gordon Brown, the British prime minister, touched down in Baghdad, the Iraqi capital, on Saturday.