Less than three years on from the 2014 referendum, Mr Brown said it was important to send First Minister Nicola Sturgeon "a message that she should focus on the day job of running our schools and hospitals, and forget about her obsession with another divisive independence referendum".
Nicola Sturgeon has refused to rule out trying for a third independence referendum within a short period if she lost her planned second vote.
The First Minister will campaign in Cumbernauld, Kilsyth and Kirkintoilloch East, Argyll and Bute, North Ayrshire, Ayr, Carrick and Cumnock, Dumfries and Galloway and Dumfriesshire, Clydesdale and Tweeddale.
MHAIRI BLACK has urged younger voters to come out and vote against the Tories in Scotland and around the United Kingdom, emphasising the danger they pose to the economic future and rights of the young.
"No matter which party you normally vote for, it's only a vote for your Scottish Labour candidate that can stop the SNP here", Mr Brown writes.
He is expected to say: "This election is our chance to say loud and clear that Scotland does not want another divisive independence referendum".
Ms Thornberry insisted Labour were "fighting to win with a majority" and would do "no deals" with other parties. Now, why I set out those dates is that that is what Theresa May is telling us right now the end of the process will be.
Labour leader Jeremy Corbyn has rejected a formal deal with the SNP to lock the Tories out of power at Westminster in the event of a hung parliament - but there is still a prospect the parties could work together informally on a vote-by-vote basis.
"I don't say that independence is a magic solution to everything", she said.
She also confirmed that plans to fast-track graduates into teaching roles could soon be put into place to help ease teacher shortages.
She said teacher recruitment challenges were "not unique to Scotland".
And Scotland is on course for a very strong turnout with 72% of people saying they will definitely vote in the election.
Ms Sturgeon told BBC Radio 4: "If there was to be a hung parliament, if the parliamentary arithmetic allowed it, then I would want the SNP to be part of a progressive alternative to a Conservative government".
Highlighting its final campaign leaflet, which contrasts a Conservative vote with a vote for the SNP, Depute Leader Angus Robertson said his party would always stand up for family budgets.
Both parties have ruled out a formal coalition deal should the election on 8 June not produce a clear victor.
"Actually what would be more helpful for Jeremy Corbyn after June 8 if the Tories don't have a majority would be to have a block of SNP MPs who are prepared to back up a fairly radical programme, given that half of it we're already implemented in Scotland anyway".