Prime Minister Jean-Claude Juncker responded by saying the country would change its constitution to reduce the powers of the sovereign, who traditionally stays above the political fray.
"Because we wish to avoid a constitutional crisis, but at the same time respect the opinion of the Grand Duke, we are going to take out the term 'approve' from article 34 of the constitution and replace it with the word 'promulgate,'" said Juncker, a move which would scrap the sovereign's formal power to block laws.
Juncker's announcement came after Grand Duke Henri, the constitutional sovereign, warned that he would not sign off on a law to legalise euthanasia if it is passed by parliament.
It also came after two hours of talks with political party leaders, leaving little doubt that Juncker had the backing for the move.
Such a constitutional change would require a two-thirds majority in parliament.
"I understand the Grand Duke's problems of conscience. But I believe that if the parliament votes in a law, it must be brought into force," Juncker said earlier, despite his own personal opposition to the bill.
Luxembourg's Justice Minister Luc Frieden said the move was designed to avert a constitutional crisis in the micro-state wedged between France, Germany and Belgium.
The Grand Duke "will no longer participate in the legislative process, he will just sign the law to mark the completion of the procedure," Frieden said.
The constitutional revision is set to be put to parliament next Tuesday, according to Green party leader Francois Bausch.
A parliamentary source said that the 53-year-old Grand Duke, in power since 2000, had informed party leaders on Monday that he would not sign the law "for reasons of conscience," in a break from the sovereign's traditional political neutrality.
"Grand Duke Henri does not intend to sign the euthanasia bill," which would "therefore not enter into force," RTL radio echoed Tuesday.
Never in Luxembourg's history has the sovereign blocked a decision agreed in parliament.
The law, which would decriminalise certain types of euthanasia, is expected to be definitively adopted by the chamber at a second and final reading this month.
The Grand Duke, a member of the staunchly Catholic reigning family, should then normally "approve and promulgate" the law, by signing it within three months.
At its first parliamentary reading in February, the draft law was narrowly approved by 30 votes for and 26 votes against.
That vote was a defeat for the Christian Social People's party, Juncker's own party, whose members strongly opposed the move, fearing it would make euthanasia an everyday event.
It was approved thanks to support from Socialist deputies within the coalition government along with opposition liberals and Greens.