The US-led coalition views the southern provinces of Helmand and Kandahar, traditional Taliban heartlands bordering Pakistan's tribal areas, as crucial to turning the tide in the nine-year war.
Gates said Monday that US and coalition forces were "well-positioned" to begin a gradual drawdown as planned in four months but has not given a number for how many US personnel could leave at that stage.
Afghan forces are due to take control of security across the whole country by 2014.
Gates arrived at Camp Leatherneck in Helmand a day after personally apologising to President Hamid Karzai over a NATO air strike last week that accidentally killed nine young Afghan boys who were out collecting firewood.
"This breaks our heart," Gates told a news conference Monday at the presidential palace in Kabul, as the US-backed Karzai looked on.
"Not only is their loss a tragedy for their families, it is a setback for our relationship with the Afghan people."
Karzai, who had already angrily rejected a public apology from General David Petraeus, the US commander of international troops in Afghanistan, told Gates he respected his words but such incidents had to stop.
The Afghan president revisited the issue in a speech Tuesday.
"We have never complained when our soldiers are killed, our police are killed," he said he had told Gates, who is on a two-day visit to Afghanistan.
"Thousands of our youths give their lives for this country and their mothers and fathers never complain -- but we do not accept civilian casualties in the hands of our allies."
The episode has underscored strained relations between Karzai's government and Western allies at a delicate moment in the conflict, shortly before Karzai announces on March 21 the areas where the transition will start.
He offered a teaser on his plans Tuesday, saying "five to six places" would be handed over to Afghan forces in the first stage, but did not specify whether these were towns, districts or provinces.
Afghan officials were not immediately reachable for clarification.
A US team is due to arrive in Afghanistan next week to begin negotiating a "security partnership" between the United States and Afghanistan beyond 2014, Gates said.
Any American presence at that stage would be a "small fraction" of the current 97,000 US troops out of a 140,000-strong international force now deployed, he added.
There have been calls from some Afghan and US politicians for permanent US bases to be established in Afghanistan and Karzai has said talks are taking place on the issue.
But Gates told Monday's press conference the US had "no interest" in permanent bases in Afghanistan.
He added it was "open to the possibility of having some presence here in terms of training and assistance, perhaps making use of facilities made available to us by the Afghan government for those purposes".
US commanders are bracing for a spring offensive from the Taliban and other insurgents but say they have piled pressure on them during a winter lull in fighting with night raids against militant leaders and efforts to disrupt supply routes.
The Taliban and other militants have been waging a bloody insurgency against international and Afghan government forces since being ousted by a US-led invasion in 2001.