Another right-of-centre party, the PSD's former coalition partner, the People's Party, has already said that it might support a referendum.
After a colloquium organised on Thursday by the PSD group in parliament at which deputies had the chance to discuss ethical, medical and legal issues relating to euthanasia and assisted dying with experts in various fields, the group's leader, Luís Montenegro, took the opportunity to send a message to all deputies and parliamentary groups.
"We shouldn't accelerate and precipitate a decision in this matter and we shouldn't rule out any decision: the decision to legislate to decriminalise, the decision to legislate increasing the penalties, the decision to do nothing, the decision to put it to a public consultation," Montenegro said. "Our position is of total openness: we don't rule out any possibility."
The radical Left Block has announced plans to table a bill to decriminalise assisted dying as soon as next week, but the PSD, Montenegro said, does not want to rush into taking a position.
"We wanted to start a discussion" with Thursday's meeting, Montenegro said, adding that an "informed" decision requires time and organisation.
He reiterated that each PSD deputy would be free to vote as they wished on the Left Block bill, but stressed that no party had laid out plans for legislation on the subject during the campaign for the 2015 general election - meaning that deputies should be even more careful.
At the PSD colloquium, three doctors taking part in the final panel all expressed opposition to moves to decriminalise euthanasia, calling instead for improved palliative care.
The president of the Portuguese Association of Bio-ethics, Rui Nunes, called on PSD deputies to propose a referendum on the subject, noting that any change in the law would represent a major alteration in public policy and arguing that this cannot depend simply on the make-up of parliament at one particular time.
By contrast, Luís Marques da Costa, professor and director of palliative care at Lisbon's Santa Maria Hospital, reported that even terminally ill patients often change their minds over time, and warned that they may lose their trust in the health system if euthanasia is brought in as a medical option.
Two out of three constitutional experts who also took part in the meeting, meanwhile, said that the safeguards in Portugal's constitution do not rule out legislation to make euthanasia legal. One of them, Maria Lúcia Amaral, argued that the justice system "cannot allow the State to impose on someone the duty to live in any circumstances".