In a speech to French ambassadors in Paris, Macron said "Europe can not rely on the United States only for its security".
He said: "This reinforced solidarity will imply a revision of the European architecture of defence and security: by initiating a renewed dialogue on cybersecurity, chemical weapons, conventional weaponry, territorial conflicts, space security, the protection of polar zones, in particular with Russian Federation".
Rasmussen said Denmark wanted to cooperate immediately and as much as possible within the limits of its defense opt-out from the European Union - one of four opt-outs put into practice in 1993 after Danes rejected full EU membership the year before.
He urged Europe to exert itself as "a trade and economic power", which defends its strategic interests and financial independence and is able to fend off the extraterritorial reach of US sanctions.
Mr Macron's plea comes after US President Donald Trump told his North Atlantic Treaty Organisation allies that all members of the defence alliance must pay their fair share of defence spending.
Macron's remarks follow a similar call for increased European Union defense cooperation last week by German Foreign Minister Heiko Maas, who has said Europe should "take an equal share of the responsibility" and "form a counterweight" to Washington in the world as Europe-U.S. relations cool.
"'America First" was a wake-up call.
His comments follow US President Donald Trump repeatedly distanced himself from the North Atlantic Treaty Organisation military alliance, which groups the United States with most of Europe and has underpinned European security since World War II.
The France Inter radio hosts did not know he would resign prior to the announcement.
At a North Atlantic Treaty Organisation summit in Brussels last month, Mr Trump called on European countries to increase their defence spending to at least two per cent of their gross domestic product - a goal that many members, including Germany, do not yet meet.
Mr Trump called on European countries to increase their defence spending.
Numerous eastern bloc members already meet that goal.
EU powerhouse Germany has given only muted backing to Macron´s ambitious plans, but his call for greater European military cooperation echoes recent comments by German Foreign Minister Heiko Maas.
"We need to take new initiatives, build new alliances", he said, according to the South China Morning Post.
In November, EU countries launched an unprecedented programme of joint military investment aimed at confronting EU security challenges. Twenty-three of the EU's 28 member nations signed up to the process, known as permanent structured cooperation, or PESCO.