State police spokesman Mukhtar Aliyu said that “unknown armed men” seized the four on the road to Abuja at 7pm local time on Tuesday.
“They engaged in a fierce gun battle with the two police escorts attached to the expatriates, who unfortunately lost their lives,” he added.
No further details were given and Aliyu said “every possible means” were being employed to rescue the four abductees and arrest the kidnappers.
A spokesman for the US embassy in Abuja said he had no comment to make when contacted by AFP. There was no immediate response from the Canadian high commission.
Kidnapping has long been a problem in Nigeria’s southern states, where high-profile individuals, including the families of prominent politicians, are frequently seized. Victims are usually released after several days once a ransom is paid.
In recent years the crime has spread across the country as the economy has stalled. A crackdown on cattle rustling has been blamed for rising numbers of abductions in the north.
In October last year, an armed gang seized four British missionaries working for a medical charity in the oil-rich but impoverished state of Delta in the south. One of the hostages was killed while the three other hostages were later released.
Also in October, the Vatican said an Italian priest was kidnapped near Benin City, the capital of Edo state, which borders Delta state to the north. He was also later released.
Last February, two German archaeologists from the Goethe University in Frankfurt were kidnapped from an excavation site in Kaduna state. The site was off the main road linking the airport north of the state capital, Kaduna city, with Abuja, 137 miles away. The pair were freed after several days.
Safety on the Kaduna-Abuja road came under intense scrutiny last year when the federal government announced the closure of the capital’s only airport for essential runway repairs.