The country's police will be carrying weapons until further notice in the main cities as well as Oslo airport.
The police in the Scandinavian country, which borders Sweden, do not usually carry guns as a matter of routine police patrols.
Finland, another Scandinavian country, has also upped its security presence on the streets with increased police patrols in the capital Helsinki.
Norway police will be armed in key areas of the country
The news follows in the wake of the truck attack in Sweden earlier today that killed three people.
A stolen truck ploughed into a crowd in central Stockholm on Friday that left three people dead and several others injured.
Oslo Police spokeswoman Marita Aune confirmed that officers in Oslo already have started carrying weapons.
The Stockholm Terror attack – in pictures Fri, April 7, 2017
The vehicle drove into crowds on Drottninggatan (Queen Street) – one of the city's major pedestrian streets, just before 3pm local time, before crashing into Åhlens Mall
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Truck rams into crowds in central Stockholm
Countries across the continent offered support and condolences to the Swedish people in what the Government said appeared to be a terrorist attack.
President of the European Commission Jean-Claude Juncker said: "An attack on any of our member states is an attack on us all.
"One of Europe's most vibrant and colourful cities appears to have been struck by those wishing it – and our very way of life – harm.
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Police investigate the Stockholm attack
"We stand shoulder to shoulder in solidarity with the people of Sweden and the Swedish authorities can count on the European Commission to support them in any which way we can."
President of the European Council Donald Tusk tweeted: "My heart is in Stockholm this afternoon.
"My thoughts are with the victims, and their families and friends, of today's terrible attack."
Armed police in Norway will patrol the cities and Oslo airport
Sweden's neighbours also expressed their horror.
Finland's Prime Minister Juha Sipila wrote in Swedish on his Twitter account: "Terrible news from Stockholm. Our thoughts are with our neighbours and friends in Sweden."
Danish Prime Minister Lars Lokke Rasmussen said in a statement: "It hurts deep into my heart that our Swedish brothers and sisters have been exposed to such an abominable attack.
"A cowardly attempt to subdue us and our peaceful way of living in Scandinavia. It is a day of mourning. But it is also a day of will … A will to fight the darkness. For every attempt to bend us we move closer. We move closer around our Swedish neighbours."
Norwegian Prime Minister Erna Solberg said in a tweet: "Shocked over the terrible attacks in the middle of Stockholm. Our brothers and sisters are hit and we share their sorrow."