Speaker Tony Smith says every aspect of yesterday's protest in parliament will be investigated and he will report back on the matter.
A 30-strong pro-refugee group labelled government MPs cowards for walking out of the lower house chamber during their protest.
Opposition Leader Bill Shorten and his MPs remained in the house while Greens leader Richard Di Natale embraced several of them as he lauded their actions.
Mr Turnbull will never be convinced parliament's public galleries should be closed, even after dozens of protesters forced a temporary shutdown of question time.
While he wasn't worried about his personal safety, the prime minister was concerned the protesters had managed to interrupt parliament, "denying democracy".
"Incidents like this are regrettable and they will happen from time to time but people should not feel they are free to interfere with the parliament," he told the Seven Network on Thursday.
