The former SNP leader and First Minister of Scotland has come under renewed pressure to give up his show with the state broadcaster since two suspected Russian intelligence agents were charged with the attempted murder of Sergei and Yulia Skripal in Salisbury in March.
Mrs May was asked about the controversy by Scottish Conservative MP John Lamont, who used at question during PMQs to say: "Given what we know about the Russian state's involvement in the Salisbury poisoning, does the Prime Minister think it appropriate that parliamentarians both current and former appear on Russian state television?"
The Prime Minister replied that "I'm sure we all have doubts about the objectivity of the reporting on Russia Today, which does remain a tool of propaganda for the Russian State."
She continued: "Decisions about appearing on Russia today are a matter of judgement for each individual but they should be clear that they risk being used as propaganda tools by the Russian state."
Mr Salmond said it was "plain daft" for the Prime Minister to "offer a comment on a show she has never even seen". He said his programme was running a series on the UK's railways, including disruption in London from the construction of the HS2 rail line, and invited Mrs May "to judge if she can detect any pro-Russian propaganda from the residents of Camden".
In her response in the Commons, Mrs May added: "I know that that is a view shared by other members of this house, including [SNP Westminster leader Ian Blackford] who's made clear he doesn't think people should appear on that station."
Mr Blackford has criticised the channel, saying RT is "a vehicle of the Russian state".
“I personally would not encourage people to go on RT,” he said last week. “It’s clear the Russian state is demonstrably implicated in the attack on the Skripals in Salisbury.
“People need to know exactly what the Russian state is doing and by extension RT is part of that.”
The SNP MP Angus MacNeil has defied the warning about RT from his group leader, saying: "I will talk to any media."