The former Scottish Secretary temporarily suspended his pro-Union 100 Streets In 100 Days tour last week amid claims that the events were being targeted by Yes supporters in a co-ordinated campaign.
A kilted No supporter played the pipes as he mounted his Irn-Bru crates to cheers outside the Royal Scottish Academy Building off the city’s Princes Street.
Mr Murphy, who was pelted with eggs as he spoke in Kirkcaldy, Fife, last week, was also greeted by a tabloid reporter dressed as a chicken and brandishing two dozen eggs.
He was heckled only once as he addressed the crowd of about 300 supporters, many sporting No Thanks badges and signs.
There was a noticeable police presence at the event, with two police cars and four officers visible.
Speaking after addressing the crowd, Mr Murphy said: “I really enjoyed it, it’s the warmest welcome a Glaswegian has ever had in Edinburgh
“Whoever turned on the noisy tap of that kind of mob mentality over the past fortnight has quietly turned it off over the weekend and I think that’s good for the referendum, and it’s great for the campaign because we can now have a really passionate debate about the future of our country.
“We can get back to talking about the pound, pensions, who’s going to pay for our public services with independence.”
Mr Murphy denied he had overreacted by cancelling his tour and insisted that he had been the subject of co-ordinated attacks.
He said: “It’s clear in the past fortnight - you can see on all the social media sites - that that was co-ordinated by the Yes Scotland offices at a local level.”
He said he was looking forward to the remaining stops on his journey but refused to comment on whether the police presence would continue.
Mr Murphy said: “I can’t go further into any of the security details of it apart from to say that everyone on both sides of this argument should be able to passionately argue their case because this is the biggest decision we’re going to take as a country.
“This is the most important decision we’re ever going to take. It’s irreversible. Once it’s done, it’s done, there’s no going back and if it doesn’t work out the way that nice man Mr Salmond tells us, we can’t take it back to the shops.
“There’s absolutely no guarantees with independence, which is why it’s important to have this style of politics and make sure all our questions are answered.”
He dismissed the suggestion that the Yes campaign has the momentum in the debate, with a new poll showing support for Scottish independence has risen eight points in a month
Mr Murphy said: “The No campaign is in the lead and if you ask me which campaign I’d rather be with - the No or the Yes campaign - then I’d rather be with the leading campaign, the patriotic No campaign.
“The thing that worries me isn’t the opinion polls, it’s the fact that with a fortnight to go we still don’t know what currency Scotland would use if we’re independent. Those are real worries.”