COPENHAGENCOPENHAGEN (Reuters) - Denmark will take part as much as possible in European defense cooperation outside NATO, Prime Minister Lars Lokke Rasmussen said after meeting France's president on Tuesday.

French President Emmanuel Macron, who said on Monday that Europe could no longer rely on the United States for its security, welcomed Rasmussen's comment, saying: "Strategically, a greater involvement from Denmark would be good news for Europe and for France."

U.S. President Donald Trump has been sharply critical of NATO, demanding that European member states share more of what he has called an unfair burden on U.S. taxpayers in funding the Western alliance.

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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.

"That's why we have agreed during this meeting (with Macron) that we on a bilateral basis will enhance our cooperation," Rasmussen told a news conference alongside Macron.

"One reason is that transatlantic relations are changing these days; we both realized that during the last summit. So we have to take greater responsibility for our own security."

Rasmussen said he believed that there would be a division of labor between NATO and Europe in the future, and said Denmark should begin to debate its EU defense opt-out.

"I think it is strange if we put Denmark in a position where we participate in the tough actions in NATO or through different alliances and then when we should invest in stabilization and rebuilding countries, Denmark has to withdraw," he said.

The opt-outs can only be changed at a referendum but Rasmussen said he would not call for such a vote before the next general election, due to be held by June next year.

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Danish voters in December 2015 rejected a government proposal to give up their opt-out from a range of EU justice and home affairs laws to keep the country inside the European police agency. Denmark later got a deal with that allowed it to continue using the Europol database.

Denmark has also opted out of the common euro currency, but its crown currency has been pegged to the euro for decades.