The My Life, My Death, My Choice campaign has handed in a 2,500 signature petition to the Scottish Parliament.
The group claimed support for a change in the law was at an all-time high.
But opponents of the bill said supporters of assisted suicide were losing the battle of public opinion.
Sheila Duffy of My Life, My Death, My Choice, said: "The petition handover today demonstrates the level of support there is for the bill across Scotland.
"As our campaign has progressed it has become increasingly clear that public support for a change in the law is at an all-time high and this issue is very much something that needs to be looked at closely."
My Life, My Death, My Choice was launched on the back of a poll that suggested that 69% of Scots wanted the Assisted Suicide bill to become law.
The group's petition in favour of the bill is the latest stage in a campaign that began at the start of the year.
Ms Duffy said: "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.
"We want to ensure that people are provided with appropriate information to make their own, individual, choices and, in certain limited circumstances, given assistance to end their life."
But a spokesman for the umbrella group Care not Killing said that the petition showed "only a fraction of 1% of the population backs the idea - hardly a groundswell of support".
He added: "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.
"The current law we have is clear and right. Through its blanket prohibition of assisted suicide it provides a strong disincentive to abuse and exploitation whilst allowing prosecutors and judges discretion in hard cases."
The Green MSP Patrick Harvie will take the legislation forward after the public consultation finishes on Friday.
A previous attempt by Ms MacDonald to pass a right-to-die bill was voted down by MSPs in 2010.
Campaigners have urged MSPs to pass the Assisted Suicide Bill which was introduced to Holyrood by the late MSP Margo Macdonald.