More than 100,000 names have been added to the SNP-backed petition since Friday, with the figure reaching 485,000 as of Monday lunchtime.
Nationalists have been emboldened in their demands for a second referendum on independence following the result of the December 12 general election, which saw Nicola Sturgeon's party win 47 out of 59 constituencies in Scotland.
The petition, hosted on the Yes.scot campaign platform, calls on Scots to sign a pledge to "help us to send a message to Westminster that now is the time for independence by inviting your friends, family and followers to pledge their support".
It continues: "We need to focus all our efforts on building an independence majority. This work will start with a major new campaign focused on Scotland’s economic potential as an independent country."
Scotland's constitution secretary Mike Russell claimed today the general election result showed the people of Scotland voted "overwhelmingly" for another referendum on independence.
But Scottish Conservative MSP Michelle Ballantyne said there would likely not be another referendum in the lifetime of the new UK parliament.
Ms Ballantyne also said that the Prime Minister would reject the Section 30 request, which would allow for the devolution of powers needed to hold a referendum.
Pamela Nash, chief executive of Scotland in Union, said: “The majority of people voted last week for parties that support Scotland remaining in the UK.
“Of those who voted for the SNP, Nicola Sturgeon herself acknowledged that many were registering a protest against Brexit and/or Boris.
“Leaving the UK is not the answer to the challenges we are facing; it would be the cause of more. That’s why a majority of people know we are stronger together as part of the UK.”