It came as Ofcom opened investigations into seven separate allegations that programming on the Russian state-funded channel RT broke impartiality rules.
The channel, which broadcasts the former First Minister's programme, has faced calls for it to be banned in the UK following the chemical attack in Salisbury, which the UK Government has blamed on the Kremlin.
None of the impartiality investigations relate to the Alex Salmond Show. However, Ofcom is already investigating whether the programme breached rules on accuracy after tweets were read out during the inaugural broadcast on 16 November which were claimed to be from audience members.
One of the messages appeared to be from a twitter account linked to the show's production team, while two others could not be traced. A footnote in the Ofcom announcement states: "We already had one open investigation relating to 'audience tweets' in the Alex Salmond Show, which we have provisionally found were not from audience members".
Mr Salmond has resisted calls from across the political spectrum to abandon his programme, saying he will not be "bulled off the air".
If RT is found to have broke broadcasting standards requiring "due impartiality" in news and current affairs programming, it could be stripped of its license to operate in the UK.
"Ofcom has today opened seven new investigations into the due impartiality of news and current affairs programmes on the RT news channel," the regulator said in a statement.
"Until recently, [RT license-holder] TV Novosti’s overall compliance record has not been materially out of line with other broadcasters."
"However, since the events in Salisbury, we have observed a significant increase in the number of programmes on the RT service that warrant investigation as potential breaches of the Ofcom Broadcasting Code.
"We will announce the outcome of these investigations as soon as possible. In relation to our fit and proper duty, we will consider all relevant new evidence, including the outcome of these investigations and the future conduct of the licensee."
In a statement, RT responded: “We are pleased to see that Ofcom has acknowledged RT’s compliance record has been in line with other broadcasters – putting to bed any of the salacious political statements and challenges made against our channel.
"Our editorial approach has not changed since the events in Salisbury, and we will be directly addressing this matter with the regulator.”
Scottish Conservative deputy leader Jackson Carlaw said: "With Ofcom stepping up its investigations into RT there is an even stronger consensus that this channel is severely biased towards Russia.
“Mr Salmond’s continuing willingness to be used as a Russian stooge is an embarrassment for himself, his party and his country.”