"One of course has to be very cautious when consulting regimes that don't live up to our democratic requirements," party leader and Swedish prime minister Fredrik Reinfeldt commented today when the newspaper Expressen published the story.
The consultant in question, Göran Lindblad, defends his work with the organisation TEAS, which several observers, including Civil Rights Defenders, say works closely with the Azer authorities.
"Azerbaijan is a new democracy on its way to what we call a democracy, but they have a long road ahead," he tells Swedish Radio.
Robert Hård, head of Civil Rights Defenders in Sweden, disagrees.
"I wouldn't say it's on its way toward democracy, there are today no signs whatsoever indicating that," he tells Swedish Radio.
Expressen also claims that Göran Lindblad is simultaneously cashing in on the Swedish parliament's income guarantee for former MPs.
"The aim of an income replacement should be to look for work and find a new income," the prime minister said.
"All Moderates should keep this in mind when they leave parliament."