Premier Gladys Berejiklian has left open the possibility of government action on gun laws in the wake of a murder-suicide that saw a Sydney father shoot and kill his two teenage children.

Jack Edwards, 15 and his sister Jennifer, 13, were killed in their West Pennant Hills home last Thursday, when they were shot by their father John, who later took his own life.

On Monday Ms Berejiklian stopped short of committing to legislative changes to NSW gun laws, but said the government was open to action, if required.

"We are taking advice from police to ascertain exactly what happened. I've already been in touch with the Commissioner," she said.