Scotland's unemployment rate remained at 4.5% over the summer, with 124,000 people seeking work, figures show.
The Office for National Statistics (ONS) also said the employment rate in Scotland rose slightly in June to August, to 73.9%.
The UK's unemployment rate rose to 4.5% over the same period, with an estimated 1.5 million people looking for work.
The Scottish government said the figures did not reflect the "full impact" of Covid-19 on employment.
ONS monthly tax figures show that across the UK there were nearly 700,000 fewer employees on the payroll in September compared with March, before the lockdown.
There were 2,329,000 payrolled employees in Scotland over the quarter, a decrease of 2.7% compared with September 2019.
BBC Scotland's business and economy editor, Douglas Fraser, said the statistics showed some evidence of "stabilisation of the labour market" during the summer.
"Lockdown was being eased, people were coming off furlough, returning to work. We were encouraged to go out and help out by eating in restaurants," he said.
"A lot of people were kept away from being unemployed, or from seeking work anyway, because they remained on furlough and they expected to be returning to their jobs at some point."
He added that the UK-wide unemployment rate saw a "significant rise" over the quarter to bring it up to the same level as Scotland.
Paul Johnson, from the Institute for Fiscal Studies, said the latest ONS figures were still "remarkably modest".
"I think we're going to see very dramatically higher levels of unemployment over the next six to nine months," he told BBC Radio's Good Morning Scotland programme.
"I think there's a good chance I'm afraid that we'll get up to levels of unemployment next year not seen since the early 1990s - and that's despite the £200bn worth of support the government has poured into the economy over the last six months."
Hospitality jobs fears
Scottish business minister Jamie Hepburn said: "These figures still do not reflect the full impact of coronavirus on employment as the Job Retention Scheme [furlough] will have offered relief to many employers and employees."
The minister said the Scottish government had recently launched a National Transition Training Fund to help people aged 25 or over who had lost their job or who were at risk of redundancy as a result of the virus.
"We are doing everything we can with the limited powers available to us to support people through this crisis - but it is essential that the UK government also plays its part," Mr Hepburn added.
On Friday, pubs and restaurants across the central belt were closed temporarily, prompting industry leaders to warn that thousands of jobs were being put at risk.
The closures were part of measures by the Scottish government to reduce the surge in Covid-19 cases across five health board areas.
UK Hospitality's executive director for Scotland, Willie Macleod, said many businesses would not survive the new measures - with a "horrific" impact on jobs.
The UK government's Scottish Secretary Alister Jack said there would be "further challenges to come" on unemployment figures.
He added: "The UK government is doing everything possible to protect jobs and livelihoods in the face of the global pandemic.
"We are supporting nearly half a million jobs in Scotland through our furlough and self-employed schemes and have committed a further £9bn to help employers keep workers on."