State police spokesman Mukhtar Aliyu said "unknown armed men" seized the four North Americans on the road to Abuja at 7:00 pm (1800 GMT) 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 used to rescue the four abductees and arrest the kidnappers.
In Washington, a State Department official referred to the abduction of only one US citizen.
"We are aware of reports of a US citizen kidnapped in Nigeria," he told AFP, speaking on condition of anonymity. "The safety and protection of US citizens overseas are among our top priorities," he added.
A State Department travel advisory for urges US citizens to "reconsider" travelling to Nigeria, warning that "violent crime such as armed robbery, assault, carjacking, kidnapping and rape is common throughout the country."
Global Affairs Canada. which manages Canada's diplomatic and consular relations, is "aware of reports of the kidnapping of two Canadian citizens in Nigeria," spokesman John Babcock said, "Consular officials in Nigeria are in contact with local authorities to gather additional information," he added.
Kidnapping has long been a problem in Nigeria's southern states, where high-profile individuals, including the families of prominent politicians, are regularly seized.
Ransoms paid
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.
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.
Many foreign missions and companies advised staff to limit their travel during the closure period, as all domestic and some international flights were switched to Abuja.
In July 2016, Sierra Leone's defence attache to Nigeria was kidnapped by men in military fatigues armed with AK-47 rifles at a fake checkpoint on the Abuja-Kaduna road.
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