Unison also wanted a guarantee that the Living Wage would automatically increase across all Scotland's Councils.
The living wage is to be introduced for almost 2, 000 of the council's lowest paid workers.
The Labour-controlled council says the living wage increase will not reduce funding for services.
The minister concluded that he would continue "to evangelise the living wage in discussions with local government".
He said although employers were within the law by not paying the living wage, there was a "moral aspect".
Boris Johnson says the same thing about the many companies that have decided to pay the living wage in London.
Barclays has paid the living wage in London since 2007, while 19 local authorities have been accredited as "living wage employers".
BBC: Duncan Smith: Welfare changes will make living wage easier
Deputy leader Adrian Ramsay said the Greens would cut fuel bills, expand the living wage and protect public services from government cuts.
So, when it comes to the living wage, politicians are really looking for a free lunch: or rather, a free pay rise.
However, one 23-year-old care worker told the BBC News website that life was tough financially - even when on the living wage.
Mr Miliband suggested firms could offered tax relief on training or capital investment, or lower business rates, in return for paying the living wage.
Mr Sawers added that he hoped other public bodies would follow suit and that the living wage would be extended to their arms-length bodies.
Whitehall contracts would only go to firms paying the living wage, while those who paid less could be "named and shamed", said the Labour leader.
BBC: Living wage: Ed Miliband pledge over government contracts
The Living Wage is calculated according to the basic cost of living in the UK. Employers choose to pay it on a voluntary basis.
Currently, just over half of Scotland's councils pay the living wage.
Mr Miliband's brother David has also backed the living wage campaign.
BBC: Duncan Smith: Welfare changes will make living wage easier
Others backing the wage include the Scottish government, which says all staff will get the living wage, and London's mayor, who said it made economic sense.
BBC: Living wage: Ed Miliband pledge over government contracts
He said rent and rates were becoming more expensive, and so were energy costs, so the living wage was an aspiration but not affordable for some employers.
The KPMG report suggested that Northern Ireland had the highest proportion of people earning below the living wage, at 24% of workers, followed by Wales at 23%.
BBC: Duncan Smith: Welfare changes will make living wage easier
However, these results apply to cases where the minimum wage stays pretty low - in other words, when it remains well below most definitions of the living wage.
Mr Park told MSPs he would bring forward a bill on the living wage to the chamber and called for the "political will" to legislate on the issue.
For example, in the UK the living wage is higher in London than it is in the rest of the country because London is more expensive to live in.
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Labour leader Ed Miliband has said if the party wins the next election it will introduce rules forcing government contracts to only be given to those firms who pay the living wage.
It is also considering introducing rules that will see Whitehall contracts awarded to firms who pay workers the living wage or above and giving Treasury-funded incentives to companies who introduce the wage structure.
BBC: Duncan Smith: Welfare changes will make living wage easier
Mr Marshall-Ascough said everyone who worked at Crawley Borough Council was on the living wage or more, and that the authority would look at ensuring companies who win contracts with it paid the living wage.
Mr Mackay agreed there the desire to have the living wage enshrined in the Sustainable Procurement Bill was felt almost completely across the chamber, but he said there must be legal certainty about securing this.
He welcomed recent steps to introduce a living wage for all directly employed Scottish government and NHS employees in Scotland and reiterated the living wage should be the norm in other sectors of the economy.
Writing jointly with Unison general secretary Dave Prentis in the Observer, the former foreign secretary suggested local authorities and other employers could be offered financial incentives for insisting private contractors pay the living wage.
BBC: Duncan Smith: Welfare changes will make living wage easier
She cannot refuse to invest in a company that does not pay the Living Wage, or have union agreements, or offshore tax haven subsidiaries, but is only allowed to apply the savings to creating the largest cash return possible.
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