Former Scottish Labour leader Kezia Dugdale has formed a new campaign group in support of remaining in the EU single market.
New party leader Richard Leonard has already faced calls for the party to back permanent single market membership at its upcoming conference.
Ten of Scotland's 73 Constituency Labour Parties (CLPs) have passed motions urging the conference to support the UK retaining permanent membership of the European single market and customs union.
UK leader Jeremy Corbyn announced last week that Labour would seek to form a "new and comprehensive" UK-EU customs union to ensure tariff-free trade after Brexit.
The new Scottish Labour for the Single Market group said it will work with trade unions and other campaigns to fight for Labour to support permanent UK membership of the European single market and customs union.
It is described as a grassroots campaign co-chaired by Ms Dugdale, MP Ian Murray and MEP Catherine Stihler.
Ms Dugdale said: "When the EU referendum took place, nobody voted to put jobs at risk, prolong austerity, or tear up our rights at work or as consumers.
"But this is precisely what the Tory Government is now doing. The Labour Party has to stop them.
"Jeremy Corbyn's welcome decision to support a customs union puts clear blue water between us and the Tories, however - if we are to leave the EU - the least-worst option for limiting the damage caused by a Tory Brexit is to also remain in the single market.
"This is the only way to tackle austerity, protect jobs, and defend our hard-won rights for workers and consumers.
"Scottish Labour can lead the way and help persuade our party to ensure the UK permanently remains in the single market."
A Scottish Labour spokesman said: "Richard campaigned to remain in the EU but he accepts the referendum result and the franchise of the referendum.
"There is no state which is a full member of the single market which is not a member of the European Union.
"Therefore in keeping with the policy laid out by Sir Keir Starmer, Labour's Brexit spokesperson, Scottish Labour will continue to seek a deal which retains the benefits of the single market, and will not support a deal which does not."
He added: "It is clear now that Scottish Labour must unite around an agenda which secures a new and progressive relationship with the European Union and protects Scotland's devolution agreement within the UK."