Mr Murphy’s comments come just a day after the SNP suspended two members for their part in a protest that disrupted a Scottish Labour event in Glasgow earlier this week.
Smart, who describes himself as a ‘lefty lawyer’ and ‘Scottish Labour Party hack’ on the social media site has attracted criticism for a number of tweets in the past, including referring to Nationalists as ‘fascist scum’.
During last year’s Commonwealth Games, he sparked fury by tweeting: “So, two black English lassies cheered all the way round Hampden. I suspect Eck is crying into his soup.”
And Mr Murphy today said that the former president of the Law Society of Scotland has been warned about his tweets.
Mr Murphy said: “We have told Ian Smart his behaviour is unacceptable. He has been left in no uncertain terms about that.”
Mr Murphy had earlier said there was a ‘world of difference’ between Mr Smart and the ‘angry mob trying to prevent democratic debate’, in reference to the protesters who disrupted the event in Glasgow city centre on Monday.
Last month, First Minister Nicola Sturgeon brought up Mr Smart’s tweets during FMQs following the revelation that SNP candidate for Edinburgh South Neil Hay had sent offensive tweets under a pseudonym.
The SNP leader challenged Scottish Labour deputy Kezia Dugdale to take action over Mr Smart.
Ms Sturgeon said: “It’s not the first time [Mr Smart’s] used remarks like that and I would invite Kezia Dugdale, before she comes to me, lecturing me on what she expects me to do about SNP members - can I just politely suggest to her that she puts her own house in order first?”