The Danish embassy in Dhaka said the prime minister had scheduled a 10-minute meeting with Kanita Maisha, 19, and Farjana Akter, 17, on Wednesday, but the meeting lasted more than 40 minutes.
As a part of the visit, Maisha and Farjana also took over the Twitter account of the Danish Minister for Equal Opportunities Karen Ellemann.
Their visit to Copenhagen was part of a worldwide campaign on the International Day of the Girl Child.
“All in an effort to highlight the challenges girls face and to promote the empowerment of young women and girls,” the embassy said in a statement reiterating the Day's message.
The embassy said Prime Minister Rasmussen was very impressed with the girls and their determination to change their country for the better.
“It has been truly inspirational to meet Maisha and Farjana today and I am proud that they are here in Denmark to shed light on the challenges that millions of girls face all over the world," it quoted the prime minister as saying at the meeting.
Danish Minister for Equal Opportunities Ellemann felt 'touched' by meeting the girls from Bangladesh.
“These are some really tough girls who do an immense and important effort to improve girl’s right to education and to counter child marriages and abuse," she said.
"It is important that young people in Denmark hear and understand the challenges that young people – especially girls - face in other parts of the world,” the minister said.
Maisha and Farjana also went to a number of Danish high schools where they spoke in front of more than a 1,000 students about child marriages and the challenges girls face in Bangladesh.
The two girls said they come from different backgrounds in Dhaka but share some of the same challenges in their everyday life, the embassy said.
They have both experienced sexual harassment and abuse in public and both are volunteers at Plan International Bangladesh.
In April this year, they met the Danish Crown Princess Mary and the Danish Minister for Development Ulla Tornaes, when the two visited Bangladesh.