Rasmussen looks to be aligning with mainland Europe's two most powerful countries following US president Donald Trump's decision last week to pull out of the 2015 Paris climate accord, reports the Politiken newspaper.
Denmark has traditionally closely allied itself to the United States.
And with the United Kingdom on its way out of the EU, Denmark would now orient itself more with the two countries that "set the tone" for the European bloc, an unnamed Danish diplomat told the newspaper.
Rasmussen confirmed that Denmark was in support of France's President Emmanuel Macron on climate after the two met in Paris Wednesday.
“I would like to reassure the French president that Denmark and the Nordic countries stand with France on this issue,” Rasmussen said.
Macron strongly rebuked Trump for leaving the Paris agreement last week, and Rasmussen has also spoken out against the change in American direction on climate.
Rasmussen is currently chairing the annual meeting of the Organisation for Economic Co-operation and Development (OECD), where the United States declined Monday to commit to a joint statement put together by Denmark, which notes the importance of an international trade system based on rules and agreements between countries.
Klavs Holm, Denmark's ambassador to the OECD, said that he regretted the US “can no longer commit to a text in support of openness and the fight against protectionism,” reports Politiken.
Prior to the meeting with Macron, Rasmussen also spoke about the French president's ambitions for the EU.
“I am completely convinced that France under the leadership of Macron will bring new energy to discussions of the EU's future,” said the Danish PM, who also spoke about the situation in the bloc following Brexit.
“We want to have a safe and open Europe that delivers tangible results on the areas that mean the most for its citizens. That is growth, employment, security and migration,” Rasmussen said.
The PM's statements reflect the agenda of a programme to be presented by Macron at an EU summit later this month, reports Politiken.
France's new government has already begun negotiations with industry representatives on extensive labour reforms, and Macron said after the meeting with Rasmussen that Denmark “in many contexts is a role model,” according to the newspaper.
“The Danish model is a source of inspiration for many others. Naturally also for France,” Macron said.
French voters go to the polls for the second and final round of parliamentary elections on June 18th.
Polls forecast that Macron's En Marche party has a strong chance of gaining the parliamentary majority it needs to be able to push through comprehensive reforms proposed in its programme.