The Conservatives have been critical of the new lower speed limit for city-centre, residential and shopping streets and have promised to suspend the roll-out of the scheme if they win power.
But on Tuesday evening the council tweeted a link to a “myth-busting” page about the 20mph cap on its website.
John McLellan, the Tory candidate in Craigentinny/Duddingston, tweeted: “Why is a piece from January being pushed now? Is council comms getting involved in the election?”
He said: “It was only when I looked at it more closely I realised it was from January 2015 - why is the council putting out a two-year-old press release just 36 hours before the election?
“It’s quite clear 20mph is a very big issue on the doorsteps. When you take away all the national stuff, it’s pretty close to roads and pavements as the number one issue.
“This press release is two years out of date and a lot has happened - like cancellation of Manchester’s 20mph scheme.
“I really do wonder what the council’s communications department think they are doing.”
Tory group leader Cameron Rose said he had emailed the council’s chief executive Andrew Kerr and asked him to remove the tweet.
“He accepted it was inappropriate and promised to take it down.”
Cllr Rose added: “I have asked them to tweet an acknowledgement they were in error. It was a public error and so it should be publicly acknowledged.”
Tory transport spokesman Nick Cook said the “myths” which the council website claimed to “bust” included matters which the Conservatives had voiced concerns about, including the effect of the 20mph limit on congestion and pollution and whether it was a “blanket” policy.
The website claims research indicates “vehicles flow more smoothly through junctions at slower speeds” and “20mph may help to reduce fuel consumption and associated emissions”.
Cllr Cook said: “There is a danger the council is seen to act in a political fashion this close to an election on one of the key campaigning issues.”
A council spokesman said: “The roll-out of the 20mph limit to residential, shopping and city centre streets was approved as council policy in January 2015 and the first of the new zones became effective in July 2016. A multi-media awareness and behaviour change campaign, a large part of which is on social media, began early summer 2016 and will continue until the roll-out is complete early next year.
“That said, we acknowledge that this has become an increasingly sensitive issue during the local election campaign and, as such, have removed the most recent tweet and agreed to put any further promotion on hold until after the election.”