It was the 'right approach to pursue this pragmatic approach', he said.
The Dane's third priority is to improve relations with the countries around the Mediterranean and Middle East, and especially in the Muslim world.
'Let me assure the governments and people (in NATO partner states in the region) that I am fully committed to building stronger relations with them on the basis of mutual respect, understanding and trust,' Rasmussen said.
NATO has invited Algeria, Bahrain, Egypt, Israel, Jordan, Kuwait, Mauritania, Morocco, Qatar, Tunisia and the United Arab Emirates (UAE) to work more closely with it on security in two groups known as the Mediterranean Dialogue and Istanbul Cooperation Initiative.
Rasmussen, who was Denmark's prime minister in 2005 when a series of cartoons in a Copenhagen newspaper with caricatures of the prophet Mohammed outraged Muslim public opinion, has already invited the ambassadors of the 11 countries for talks on future cooperation.
The cartoons controversy is 'an element of the past', he stressed, saying that he was looking forward to working with Muslim leaders in Afghanistan, in particular.
The Danish politician also confirmed that he had appointed former US secretary of state Madeleine Albright to lead a group of political and diplomatic experts in debating a new security strategy for NATO to guide its planning over the next decade.
And Rasmussen said that he wanted to see NATO scale back its Kosovo peacekeeping force, KFOR, by the end of his tenure, set up a permanent anti-piracy force in the Gulf of Aden and improve cooperation with the European Union.
To that end, among his very first diplomatic efforts will be a visit to Turkey and Greece, whose row over Cyprus has long poisoned NATO-EU cooperation.
Earlier on Monday, NATO welcomed its 12th secretary general as Denmark's former prime minister Anders Fogh Rasmussen arrived for his first day in the organisation's top job.