Edinburgh City Council said it planned to start work on the streets this week.
Mr Matheson told MSPs he would provide 100 per funding for the new “Spaces for People” schemes.
He said: “I very much hope local authorities come forward with bold and ambitious plans”.
The move comes after The Scotsman revealed the initiative last week.
Mr Matheson said major cities already had “detailed plans in place”.
He said: “Local authorities can implement temporary measures very quickly...in a couple of weeks.”
Mr Matheson said cycling had increased by 35 per cent compared to the February average.
Walking had also increased after dipping in the first week of lockdown.
However, he warned that if people simply switched to car travel when the lockdown was eased, there would be “gridlock”.
Public transport use has been cut by 90-95 per cent.
But Mr Matheson said to ensure physical distancing, there would be only 10-25 per cent of the normal space available on buses and trains when the lockdown restrictions were eased.
‘Agility and pace’
Transport Scotland said the £10m funding was being reallocated from existing spending on walking and cycling, or “active travel” improvements.
In a statement issued to coincide with the announcement, Mr Matheson said: “I’m pleased we are able to put forward a package of support for our local authorities to implement temporary active travel measures, helping to ensure that people can walk, cycle and wheel during this public health emergency whilst physically distancing and keeping safe from traffic.
“I have written to every local authority in Scotland to advise them that the ‘Spaces for People’ initiative is designed with agility and pace in mind.
“Our communities need this support quickly, especially with the welcome increases in cycling we are seeing across the country.
“At the same time, almost every journey starts and ends on our pavements in some way, and so it is vitally important that people can physically distance for those essential trips or for exercise.”
Edinburgh City Council is expected to announce its plans tomorrow.
Leader Adam McVey said: “We’ve been preparing plans to take this forward.
‘Changes this week’
“Expanding walking and cycling provision in Edinburgh will help residents when going outside for their once a day exercise or get to the shop to buy essentials.
“We’re hearing clearly the need to protect people’s health and safety during the current coronavirus outbreak and the desire to move forward quickly.
“We’ve been working closely with the Scottish Government to develop a range of measures to support this and will share these very soon but we are looking to start implementing changes on the ground this week.”
Glasgow City Council sustainability and carbon reduction convener Anna Richardson said: “We now have a strong endorsement for the use of temporary measures for walking and cycling that support physical distancing.
“We are already working hard to identify the projects in Glasgow that we can implement quickly.
“We will look closely at the new government guidance to understand how we may be supported in implementing these measures and seek to secure the available funding as soon as possible.”
Scottish Conservatives transport spokesman Dean Lockhart said: ’I encourage all local authorities to accelerate plans they have for any such measures.
“However this should not be a substitute for making sure roads are continuing to be maintained and potholes fixed.’’
Scottish Greens environment spokesman Mark Ruskell said: “It’s vital all local authorities make use of this important support as quickly as possible, looking at where pavements can be widened or pop up cycle routes can be installed, to ensure as many people as possible can travel by foot or by bike safely, and that necessary social distancing can take place.
“While this support has been announced in response to a national emergency, there are many places where it will be desirable for these initially temporary measures to become permanent.
“It is incumbent on us all to ensure that we make our towns and cities healthy places for the long term.”
Lothian Labour MSP Sarah Boyack said: “The increase in the numbers of people walking and cycling show that there is an appetite for safe spaces that enable social distancing, and widening the pavement and roads is certainly needed.
“However, the surfaces must be safe also, so I’d like to see progress being monitored to ensure we properly respond to this increase in demand, and safely enable greater levels of active travel for the future.”
Dr Adrian Davis, professor of transport and health at Edinburgh Napier University, said: “This is a welcome and important step in supporting the increasing active travel levels since the start of the pandemic.
“This funding is important for health and well being but also in helping to lock in the benefits of increasing active travel in the longer term challenge of transport sector decarbonisation.”
John Bynorth, policy officer for campaigners Environmental Protection Scotland, said: “It’s great to see Scotland following the lead of cities like Milan and Berlin and pushing ahead with temporary ‘pop up’ measures and infrastructure to encourage social distancing for the many cyclists and pedestrians who have poured onto our streets in recent weeks.
“With spikes of up to 215 per cent in the number of people cycling as their daily form of exercise in places like Dunfermline, and other large rises from Dundee to East Renfrewshire, Stirling and West Lothian, this reallocated funding will give people additional peace of mind as they cycle or walk to buy essential supplies, exercise or travel to their employment as key workers.”
‘Realise the urgency’
Lee Craigie, The Scottish Government-appointed Active Nation Commissioner for Scotland said: “Access to safe, pleasant places to exercise is good for everyone’s physical and mental health but it has taken this crisis for towns and cities across the world to realise the urgency with which space for walking, running, cycling and wheeling is needed, and especially in our urban areas.
“I welcome wholeheartedly the Scottish Government’s new guidance and funding measures so that local authorities might more easily reallocate space in favour of people being active.”
John Lauder, deputy chief executive of path developers Sustrans, which has assisted with the plans, said: “It’s clear people across Scotland want to do the right thing during this Covid-19 crisis.
“They want to look after their physical and mental health.
“They also want to make sure that they are keeping to physical distancing guidelines while still being safe on our streets.
“The ‘Spaces for People’ programme will allow that.”
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