The helicopter crash came as an Afghan university official identified two Americans killed in a shooting at a Kabul hospital earlier this week, the latest incident of local security forces opening fire on those they are supposed to protect.
The cause of the helicopter crash was not immediately known. Kandahar provincial police spokesman Zia Durrani said the helicopter went down in the province's Takhta Pul district in the southeast, about 50 kilometers (31 miles) from the Pakistani border. He said five international troops were killed but did not know what caused the crash.
The coalition said it was investigating the circumstances of the crash but said it had no reports of enemy activity in the area. The United Kingdom's Defense Ministry confirmed that the helicopter was British, but could not confirm the nationalities of the dead.
A Taliban spokesman claimed in a text message to journalists that the insurgents shot down the aircraft.
"Today, the mujahedeen hit the foreign forces' helicopter with a rocket, and 12 soldiers on board were killed," spokesman Qari Yousef Ahmadi said. The insurgents frequently exaggerate death tolls in their attacks and falsely have claimed responsibility for incidents before.
The last deadliest day for coalition forces was Dec. 17, 2013, when a helicopter crash killed six U.S. service members.
Saturday's deaths bring to seven the number of international troops killed this month. So far this year, 23 have been killed, according to an Associated Press count, a far lower number than previous years as international troops have pulled back to allowed Afghan security forces to take the lead in security operations.
The NATO force is preparing to withdraw its troops from Afghanistan at the end of this year, 13 years after the U.S.-led invasion to topple the Taliban's hard-line Islamic regime for sheltering Osama bin Laden and other al-Qaida leaders.
Violence has increased in Afghanistan ahead of the NATO withdrawal and also in the weeks leading up to the country's April 5 election. Preliminary results of the vote are due to be announced later Saturday.
Recently, there have been a number of so-called "insider attacks" - incidents in which Afghan security forces fire on their comrades or foreign trainers or civilians. Thursday, an Afghan police security guard opened fire on foreigners as they entered the grounds of Cure International Hospital, killing three people, including pediatrician Dr. Jerry Umanos of Chicago.
On Saturday, Kabul University vice chancellor Mohammad Hadi Hadayati identified the other two Americans killed in the attack as health clinic administrator Jon Gabel and his visiting father, Gary, also from the Chicago area. Jon Gabel's wife, also an American, was wounded, Hadayati said.
"We have lost a great man, a great teacher, a man who was here only to serve the Afghan people," Hadayati said.
Jon Gabel worked for the U.S.-based charity Morning Star Development and ran a health clinic at Kabul University, teaching computer science classes in his spare time, Hadayati said. Jon Gabel's parents were visiting from Chicago, and Hadayati had lunch with the whole family the day before the attack.
"I was very honored to meet Jon's parents," Hadayati said. "Both his mother and father were so proud of their son."
The Gabel family went the next day to Cure hospital to meet Umanos.
What prompted the police guard to fire on the Americans was not clear. The Interior Ministry released a statement Saturday identifying the attacker as an ordinary police officer from Kabul's District 6 and not a member of the Afghan Public Protection Force, as was initially reported. The APPF is a separate police unit created to protect foreign compounds.
The Afghan police guard shot himself in the stomach after the attack but was saved by the Cure hospital staff and is in custody at a police hospital.
Jon Gabel's employer, Colorado-based Morning Star Development, has four medical clinics and several training centers across Afghanistan, according to its website.
In 2012, an American doctor working for Morning Star and two of his colleagues were abducted while returning from a clinic in eastern Kabul province. The American, Dr. Dilip Joseph, was rescued by a U.S. military operation that resulted in the death of a member of the Navy's Seal Team Six, the same unit that killed bin Laden a year earlier in Pakistan. Joseph's two colleagues were later released and were never identified.
Associated Press writers Mirwais Khan in Kandahar, Afghanistan, and Jill Lawless in London contributed to this report.