Marine Gen. Joseph Dunford called Karzai late Thursday to express "deep regrets for the incident and any civilian casualties," the commander's spokesman said.
Karzai condemned the attack, which also wounded two women earlier Thursday, and said all airstrikes and foreign raids on Afghan homes must stop if the United States expects him to sign the pact that would allow thousands of Americans to stay in the country beyond a 2014 withdrawal deadline.
"This attack shows that American forces do not respect the safety of the Afghan people in their homes," Karzai said in a Dari-language statement on his website.
The two governments have agreed on a draft bilateral security agreement and it was approved by a consultative Afghan council known as a Loya Jirga. But Karzai shocked the assembly and the Americans when he announced he would not sign the deal but would instead leave that up to his successor following April 5 elections. The 2,500-member Loya Jirga had also demanded it be signed by the end of next month.
The Obama administration has been trying to persuade Karzai to change his mind and sign the deal by the end of the year in order to allow enough time to make preparations for a continuing presence after the NATO and U.N. mandates for foreign troops in the country expires at the end of next year.
In the phone call, Dunford talked to Karzai directly and "expressed deep regrets for the incident and any civilian casualties assured Karzai that an investigation would be conducted into Thursday's airstrike, which the Afghan president said was carried out by a drone in southern Helmand province.
"He talked to President Karzai directly, expressed deep regrets for the incident and any civilian casualties, and promised to convene an immediate joint investigation to determine all the facts of what happened," Dunford's spokesman Col. David Lapan said in an email.
The coalition, known as the International Security Assistance Force, said the airstrike had killed an insurgent on a motorbike in Helmand and also promised to investigate Karzai's claims that it also killed a child and injured two women.
Civilian deaths at the hands of U.S. and allied soldiers have been one of the main sources of contention in increasingly tense relations with Karzai over the years, although such killings have fallen off sharply in recent years following stricter NATO guidelines on the use of air power against ground targets.
The Taliban and other insurgent groups are blamed for the overwhelming majority of civilian casualties, most of which are caused by roadside bombs targeting Afghan or foreign forces.
Insurgents also have carried out attacks against government and elected officials as well as people working for the administration.
In one such attack Friday in Kabul, a suicide bomber with explosives hidden in his turban wounded a member of parliament at his home.
The attacker pretended to be a constituent, then blew himself up when he entered the home of Hamidullah Tokhi, a lawmaker from southern Zabul province, Kabul police chief Mohammad Zahir said.
Tokhi, who has been a vociferous critic of the Taliban and fought against them when they ruled the country, was hospitalized but was not seriously wounded, according to the police chief. No group immediately claimed the attack, though the Taliban previously have used bombs hidden in turbans to carry out suicide attacks.
Elsewhere in the south, a suicide bomber also tried to attack a NATO convoy but missed, instead killing a child and wounding three passers-by in Kandahar, provincial spokesman Jaweed Faisal said
Another suicide car bomber killed a guard and wounded three others in an explosion at the front gate of the offices of Afghanistan's National Directorate for Security in the Helmand provincial capital of Lashkar Gah, local government spokesman Omar Zawaq said.
Associated Press writrs Amir Shah in Kabul and Mirwais Khan in Kandahar contributed to this report.
Follow Patrick Quinn on Twitter at www.twitter.com/PatrickAQuinn
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.