Gates, whose visit was not announced in advance, will meet President Hamid Karzai, who complained angrily last week after nine Afghan children were mistakenly killed by helicopters from the NATO-led International Security Assistance Force (ISAF).
Karzai will soon unveil a timetable for the start of a handover of security responsibility from foreign forces to Afghans. The process is to begin in July and be complete by 2014. U.S. officials said it would be the focus of Gates's trip.
Gates is expected to visit parts of southern and eastern Afghanistan where NATO commanders say they have weakened the Taliban and created "bubbles" of security they hope to link up.
But civilian casualties have clouded the relationship and diverted attention from transition plans, with blunt exchanges between Karzai and U.S. leaders after a string of recent accidental killings, mainly in remote eastern provinces .
Karzai has said a rare and candid apology by ISAF commander General David Petraeus was "not enough". The boys were killed while collecting firewood in a volatile eastern province.
U.S. President Barack Obama has also expressed his "deep regret" but Karzai told a meeting of security advisers on Sunday, which Petraeus attended, that civilian casualties caused by foreign troops were "no longer acceptable".
Petraeus again apologised for the killings, saying they werea "great mistake", according to a statement released by the presidential palace.
Karzai in turn said such casualties were the main cause of strained relations between the United States and Afghanistan, the statement said.
Gates visited a military hospital at the vast Bagram base north of Kabul soon after arriving but had no immediate comment on civilian casualties.
"You've had a tough winter and it's going to be a tougher spring and summer, but you've made a lot of headway and I think you've proven with your Afghan partners that this thing is going to work," he told troops at the base.
Major General John Campbell, commander of NATO-led forces in eastern Afghanistan, said 90 percent of civilian casualties in his area were caused by insurgents. Of the rest, most came during "escalation of force" incidents such as when a car failed to slow down as instructed at a checkpoint, he told reporters.
He said an ISAF base had come under attack in the area where the boys were killed and his forces had responded.
Hundreds of Afghans chanting "Death to America" gathered in the capital on Sunday in protest. There have been at least four similar incidents, mainly in the east, in the past three weeks.