George Kerevan posted a message on Twitter during a Commons speech by Mr Benn's son, Hilary, where he spoke passionately in favour of airstrikes.
Alex Salmond later said in a radio interview that Mr Benn would be "birling in his grave" at the speech.
Tony Benn's granddaughter Emily said the comments were "deeply offensive" and "simply not true".
In messages posted on Twitter, the Labour councillor asked both men to retract their statements.
Fellow SNP MP Stewart McDonald said it was "repulsive" for anyone to use the phrase "spinning in his grave".
A number of tweeters used the words following Mr Benn's Commons address, before Mr Salmond used a version of it in an interview with LBC.
The shadow foreign secretary was given a standing ovation from parts of the Conservative and Labour benches after delivering a 14-minute long speech backing military intervention.
The speech and the applause which followed drew criticism from a number of SNP MPs.
East Lothian representative George Kerevan posted: "Benn summing up for Labour but voting with Tories. Benn's father must be turning in his grave."
Emily Benn, Tony Benn's granddaughter and Hilary's niece, posted a reply to Mr Kerevan, saying: "Your last sentence is deeply offensive and simply not true. I hope you examine your conscience and retract it."
Although Mr Kerevan did not reply to Ms Benn, he did later note that Mr Benn had made "a great speech", adding: "Bet on Benn as a replacement for Corbyn."
Ms Benn directed a similar message at Mr Salmond following his interview.
Glasgow South MP Mr McDonald posted on Twitter: "I voted differently to Hilary Benn. Using his father's death to make a political point - 'spinning in his grave' - is repulsive."
He also said: "Hilary Benn and I disagree, but he gave a respectful and powerful case for what he believes in."
The government motion to approve airstrikes in Syria was approved by 397 votes to 223. All SNP MPs voted against the motion, while Labour was split on the issue.
Although Tony Benn spoke strongly against military intervention in the Commons on a number of occasions, he served in the Home Guard during World War Two and later enlisted in the Royal Air Force, where his father and brother also served.
Two SNP MPs have been criticised for comments about Tony Benn "turning in his grave" during the Syria debate.