It is understood officers have been carrying the Glock pistols in the city centre as recently as yesterday.
They were seen talking to a man in George Square at around 11am with the weapons on display.
The officers are understood to be dedicated firearms officers, who were assisting regular city officers with routine duties.
Graeme Pearson, Labour MSP and former top cop, said: "I don't think it has been handled properly even to decide whether its a good idea or not.
"The way the decision has been taken has removed any opportunity for proper scrutiny of why it is necessary.
"I have written to the cabinet secretary Kenny MacAskill twice now and I will be returning to the issue when Parliament is back in a couple of weeks time.
Shettleston MSP John Mason said: "My feeling would be that we don't want to see ¬police regularly armed in the street.
"The danger is that it moves society in the ¬direction of more use of guns and we don't want to see that.
"I accept that during the Games the security is at a ridiculous level and that's how it is going to be for the next few weeks. I don't want to see regularly armed police on the streets, I don't think it's necessary or desirable."
A Police Scotland spokesman said: "There are currently 275 dedicated armed firearms officers deployed on a shift basis across the whole of the country - less than 2% of the total number of Police Scotland officers.
"Only a small number will actually be deployed across Scotland at any one time. When there is no requirement to use their specialist skills, they are available to support local policing teams by patrolling and dealing with incidents."