Civilian casualties caused by foreign forces while hunting militants have been a major source of tension between Karzai and his Western backers, and the timing of Gates's arrival for talks with the Afghan leader could not have been worse.
Gates flew into the Afghan capital from Iraq, where he attended ceremonies to mark the end of US combat operations.
That milestone has thrown the US military focus back onto Afghanistan, where violence has reached its worst levels since the Taleban were ousted in 2001, despite the presence of almost 150,000 foreign troops, most of them American.
Civilians have borne the brunt of the violence.
Gates will also meet General David Petraeus, commander of US and NATO forces in Afghanistan and US ambassador Karl Eikenberry, as well as visiting US troops.
Thursday's attack happened in the Rostaq district of Takhar, a spokesman for the provincial governor said, a province in the north near Tajikistan that has been relatively peaceful, unlike areas in the south and east where the resurgent Taleban are most active.
Spokesman Faiz Mohammad Tawhidi said the candidate, Abdul Wahid, and some of his supporters were wounded in the air strike. He said he had been told of the strike by security officials.
A statement issued by the presidential palace some hours later said NATO aircraft had conducted the strike.
"The president of the Islamic Republic of Afghanistan ... strongly condemned this attack, saying air bombardments in the villages of Afghanistan will only end up killing civilians and will not be effective in the fight against terrorism," it said.
At about the same time, a statement issued by the NATO-led International Security Assistance Force said coalition forces had conducted a precision air strike against a senior member of the militant group the Islamic Movement of Uzbekistan.
It said coalition aircraft conducted a precision strike against one vehicle traveling in a six-car convoy.
It said "initial reflections" indicated eight to 12 insurgents were killed or wounded, including a Taleban commander.
"We're aware of the allegations that this strike caused civilian casualties and we'll do our best to get to the bottom of the accusations," the statement quoted US Marine Corps Major General David Garza as saying.
"What I can say is these vehicles were nowhere near a populated area and we're confident this strike hit only the targeted vehicle after days of tracking the occupants' activity," it said.
There are no foreign troops stationed in Takhar, according to an ISAF troop distribution map, (www.isaf.nato.int), but German units are based in Kunduz to the west and Badakhshan to the east.
Last September, a US air strike called in by German troops killed scores of people in Kunduz, at least 30 of them civilians. The strike led to the resignation of the German defense minister.
In the southeast, Afghan and coalition troops fought off an attack on a combat outpost in the Bermel district of Paktika province near the border with Pakistan, killing at least 20 insurgents in air strikes, ISAF said.
Last Saturday, more than 30 insurgents were killed when they launched brazen pre-dawn raids on two foreign bases in eastern Khost province. No ISAF troops were killed in either incident.
Foreign military deaths in Afghanistan have reached record levels this year, with at least 490 killed so far this year compared with 521 in all of 2009, according to monitoring website www.iCasualties.org and figures compiled by Reuters.
Two more US troops were killed in insurgent attacks in the east and south on Thursday, ISAF said.
Increased violence is already threatening security for the Sept. 18 parliamentary poll, with four candidates and up to 13 campaign workers and supporters killed by suspected insurgents in recent weeks.
Last month, a United Nations report said civilian casualties had risen by 31 percent in the first six months of 2010 compared with the same period last year, with more than three-quarters of them caused by insurgents.
The number caused by "pro-government forces" dropped dramatically, the UN report said, mainly because of a reduction in those caused by aerial strikes after commanders tightened engagement rules.
The Sept. 18 election is seen as a crucial test of stability for Afghanistan and for the US-led Afghan war ahead of President Barack Obama's strategy review in December.