They called for improvements in social security, better jobs and more investment in areas such as housing and transport.
Crowds gathered outside Holyrood on Saturday morning, holding placards and signs as they marched through the city towards a rally at the Meadows.
John Swinney had earlier issued a supportive message to those taking part, saying it is “really welcome to see people campaigning for a positive vision of hope for the future”.
Poverty Alliance chief executive Peter Kelly, one of the march’s organisers, said those taking part wanted to see better from both the Scottish and UK governments.
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He told the PA news agency: “We’ve seen some progress in Scotland in relation to child poverty, but it’s been nowhere near what’s been required.
“Child poverty is actually falling in Scotland and that’s great news, but it’s something we need to build on and not just rest on our laurels.”
The Child Poverty (Scotland) Act 2017 set targets to cut child poverty to 18% by 2024/25 and to 10% by 2030/31.
Earlier this month the Joseph Rowntree Foundation warned that these targets were set to be missed by a “large margin”.
Child poverty in Scotland is lower than any other part of the UK and the only rate which is falling, but the Scottish Government still missed its statutory interim target to reduce the rate below 18% by last year, with the figure at 23%.
Mr Kelly said there is “so much more to do” to tackle child poverty.
Asked if Scots would be willing to pay more taxes to fund these efforts, he said: “Governments need to show that the money that they’re raising now is making a difference.
“Investing in some of the policies that we’re talking about today should help with that.”
Before the march, the First Minister offered his “best wishes” to those taking part.
He added: “Of course those marching today are right that too many people are living in poverty and too many people – many of them in work – are struggling to make ends meet.
“In a country as rich as Scotland, that is simply not acceptable to me.
“In Scotland, we have managed to make good progress – child poverty is falling here while rising in the rest of the UK, and stands at a 30-year low.
“But too often we find ourselves held back by decisions made at Westminster which make matters worse.”
A UK Government spokesperson said: “We are determined to bring down poverty. We’ve uprated benefits, increased the national minimum wage, are supporting 700,000 of the poorest families by introducing universal credit changes and will publish an ambitious strategy later this year to tackle child poverty.
“The UK Government is also investing more than £1.8 billion to deliver economic growth and a decade of national renewal for communities the length and breadth of Scotland.
“We are working closely with and supporting the Scottish Government through the largest real-terms settlement in the history of devolution for spending on policies that are key levers to improving living standards.”
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