The 5,000-signature document was taken to the Scottish Parliament.
Dumfries and Galloway Council wants to house the hoard in a new gallery being built in the region.
However, National Museums Scotland is also bidding to host the artefacts. A meeting takes place on Thursday to discuss their fate.
The objects were discovered by a metal detectorist in Dumfries and Galloway in 2014.
The Galloway Viking Hoard (GVH) group is backing the council's bid to ensure they end up in Kirkcudbright.
Cathy Agnew, who chairs the campaign, said: "The message from Galloway, Scotland and around the world is very clear - the hoard was buried in Galloway for safekeeping 1,000 years ago and that is where its home should be.
"We have huge support from the general public, academics, politicians of all parties and many others.
"It would be a travesty if their voices were ignored."
National Museums Scotland has said it believed it had put forward a "mutually-beneficial and positive proposal".
It would allow part of the hoard to go on display permanently in Kirkcudbright and the entire collection to be hosted, on occasions, by the gallery.
The Scottish Archaeological Finds Allocation Panel meets this week to discuss the hoard's future.
It will then make a recommendation to the Queen's and Lord Treasurer's Remembrancer on where the treasure should end up.

18 June 2016 Last updated at 13:53 BST
The capsule, carrying Tim Peake, Tim Kopra, and Yuri Malenchenko, touched down in Kazakhstan at 10.15 on Saturday morning.
Tim described the journey back to Earth as "the best ride I've been on ever".

The 20-year-old was granted a work permit by the Home Office after a hearing in London on Tuesday.
"I'm feeling very happy, it's a very important step in my career," Coutinho told Liverpool's official website.
"Liverpool is a great club with great players. We've always heard about Liverpool's history in Brazil. I know they believe in me and my football."
Southampton were also interested in Coutinho, who becomes Liverpool's second signing of the transfer window following the capture of striker Daniel Sturridge from Chelsea at the beginning of the month.
Playmaker Coutinho, who has one cap for Brazil, is a product of Vasco da Gama's youth system.
He was bought by Inter in 2008, at the age of 16, for €4m, although the Serie A side immediately loaned him back to Vasco, because foreigners are prohibited from playing professional football in Italy until they are 18.
However, he struggled to make an impact when he returned to Italy and spent half a season on loan at Spanish side Espanyol in January 2012 before attracting strong interest from Liverpool.
"We're always delighted when we get the players we go after," said Liverpool managing director Ian Ayre.
"It has been a successful transfer window for us, coming off the back of acquiring Daniel Sturridge from Chelsea and now Philippe from Inter Milan.
"I think that bodes well for us for the rest of the season and the future."

The Assembly Speaker says support for the Commonwealth is not part of his personal politics.
However, he said he wanted his approach during his time as Speaker to be about "respect".
He did not comment on whether Ireland should become part of the Commonwealth.
"In upholding the independence and impartiality of the Speaker, my approach during my time in office is going to be one of respect," he added.
"Involvement in the Commonwealth Parliamentary Association has naturally not been part of my political life in the past.
"However, I will represent all sides of the House as any Speaker should and I intend to respect and acknowledge the culture and traditions of all sides of the assembly chamber.
"Taking up this position is a first step in demonstrating that approach.  I look forward to hosting next week's event to mark Commonwealth Day and its theme of encouraging youth participation in our democratic system."
A petition has been delivered seeking to ensure a hoard of Viking treasure discovered in Galloway goes on display in Kirkcudbright.
[NEXT_CONCEPT]
After six months on the International Space Station, Tim Peake returned to Earth with a bump in the Soyuz capsule.
[NEXT_CONCEPT]
Liverpool have completed the £8.5m signing of Brazilian midfielder Philippe Coutinho from Inter Milan.
[NEXT_CONCEPT]
Sinn Féin's Mitchel McLaughlin has announced he will take up the position of President of the NI Assembly Branch of the Commonwealth Parliamentary Association (CPA).