The Netherlands was the world's first country to legalise gay marriage in 2001, and now it is finally extending that right to the royal family.

Prime Minister Mark Rutte has said that the heir to the throne can marry a person of the same sex and not give up their right to the succession.

Lawmakers asked Rutte to rule on the situation after a book by a constitutional lawyer about Crown Princess Amalia, 17, said she would in theory be excluded from the succession were she to marry another woman.

"The cabinet believes that the heir can also marry a person of the same sex and sees no obstacle to a law permitting a marriage of an heir to a person of the same sex," Rutte said in a letter to parliament on Tuesday.

"The cabinet therefore does not see that an heir apparent or the monarch should renounce the throne when he/she would like to marry a same-sex partner."

Amalia, the eldest daughter of King Willem-Alexander and Argentine-born Queen Maxima, has made no comment about the issue or her personal life in general.

While gay marriage has been legal in the Netherlands for two decades, royal weddings need the consent of parliament.

But whether any children from a gay royal marriage would themselves be eligible for the succession was "a bit more complicated", Rutte said.

"There is the constitution for succession, which could be in conflict with family law," he told NOS television.

The government and parliament could examine the issue if it arose, he added.

Dutch commentators hailed the decision on the direct heir.

"What Rutte is now writing about an heir to the throne who wants to marry someone of the same sex fits in with the zeitgeist," political commentator Frits Wester was quoted as saying by broadcaster RTL.

The Dutch royal family has itself been trying to adapt to changing times.

Princess Amalia in June waived her right to a yearly income of 1.6 million euros ($1.8 million) because she was "uncomfortable" receiving it before taking on full royal duties, while other students were struggling financially.