Campaigners presented a petition signed by 2,500 people calling on MSPs to pass the Assisted Suicide Bill.
The petition was brought to the Scottish Parliament by the My Life, My Death, My Choice campaign group and presented to Green co-convener Patrick Harvie.
Mr Harvie is taking the Bill forward on behalf of former independent MSP Margo MacDonald, who died in April following a long battle with Parkinson's disease.
He is supported by Conservative MSP Jackson Carlaw, Labour MSP Mary Fee and SNP MSP Bill Kidd.
Mr Harvie said: "It is great to know there is public support for this - we have seen it in opinion polls - but it is really important that we can give people a way to lend their support.
"We know there are mixed views in Scotland about this but the majority seems very clearly in favour of a change in the law.
"We want to listen to all sides of the argument, take seriously the concerns of those people who are not yet convinced, but also move forward with the principle of it."
Ms MacDonald failed to get a previous Assisted Suicide Bill through the last parliament, but was re-elected in 2011 on a mandate to resurrect the Bill.
Commenting on the prospect of the legislation passing this time, Mr Harvie said: "I really don't know whether we will reach a majority - we might do.
"There are many new members in the Scottish Parliament who perhaps weren't part of the debate before.
"We have also learned lessons from the previous Bill - this is a better Bill, some of the concerns have been addressed in the redrafting."
The petition comes as the deadline for submissions to Holyrood's Health and Sport Committee consultation on the Bill comes to a close on Friday.
The campaign was launched at the start of the year on the back of a poll which showed that 69% of Scots voters want the Bill to become law.
Campaigner Sheila Duffy said: "I think the politicians are lagging behind public opinion.
"There is a lot of cross-party support but there is no doubt this Bill faces difficulties and hurdles, and it is controversial."
She added: ''Over the last few months we have spoken to people across Scotland. People of all ages and ethnic backgrounds; from across the political spectrum; of different social and ethnic groups and of different religious beliefs.
''They have all told us the same thing: they want to have this choice should they ever find themselves in this intolerable position.''
The Free Church has condemned plans to allow healthy 16-year-olds to make assisted suicide pledges.
They claim patients suffering from chronic diseases like diabetes and multiple sclerosis "could be pressurised into assisted suicide".
Rev Dr Donald MacDonald, a former surgeon who has multiple sclerosis, condemned proposals allowing 16-year-olds to make a "preliminary declaration" of intent for assisted suicide.
"This opens the door to encouraging thoughts of suicide at a vulnerable age, as well as softening up society to accept suicide as an acceptable way out of problem situations," he said.
A spokesman for the umbrella group Care Not Killing said that "supporters of assisted suicide are losing the battle of public opinion".
He said: "This petition shows that only a fraction of one per cent of the population backs the idea - hardly a groundswell of support.
"They have only managed to gather 2,500 signatures.
"Allied to this, their own recent poll showed fewer people - 4% less - support the concept now than when they launched a similar Bill in 2010, the last time MSPs discussed assisted suicide."