The fighting in Kumanovo, close to the northern borders with Kosovo and Serbia, left another 20 injured.
Interior ministry spokesman Ivo Kotevski said that the "terrorist group" was armed with bombs and automatic rifles.
He added that it had been planning attacks on state institutions.
Mr Kotevski said that the "well-trained" group was putting up violent resistance and that the operation against it was continuing.
"This is a risky operation because it is an area with narrow streets and police need to perform house-to-house searches very carefully," he told the AFP news agency.
Police armoured vehicles have reportedly helped seal off a suburb of the town, which lies some 40km (25 miles) north of the capital, Skopje.
Witnesses have reported hearing intense shooting there since early on Saturday.
Helicopters are reported to be still circling the town and smoke can be seen rising from several houses.
Several police officers have been taken to hospital with serious injuries, according to MIA news agency. It was not immediately clear if there were any civilian casualties.
Mr Kotevski said that some residents of the Diva Naselba neighbourhood had been sheltering the armed group which had entered the country illegally.
The mayor of the town, Zoran Damjanovski, has urged local people to remain calm.
Local media say that the area of Kumanovo at the centre of the fighting mainly inhabited by ethnic Albanians.
In 2001, rebels demanding greater rights for the ethnic Albanian minority launched an uprising against the government.
Further conflict was averted by a peace agreement, which guaranteed ethnic Albanians greater recognition, but tensions have continued to simmer.
Macedonia's President Gjorge Ivanov has cut short a visit to Moscow and is returning to Macedonia to deal with the incident.
The government is already under pressure over claims of illegal wire-tapping and the alleged cover-up of the death of a man in 2011.
Thousands of protesters clashed with riot police in the capital on Wednesday.
Macedonia's political crisis dates back to last year's elections, when an opposition party made allegations of electoral fraud, denounced the government as a dictatorship, and boycotted parliament.
At least five police officers have died in clashes in Macedonia with an armed group from an unidentified neighbouring state, say officials.