Mr Morris quizzed justice secretary Chris Grayling about what action the Government was taking a year after the murder of Leasowes High School pupil Christina Edkins and a week after the fatal stabbing of a teacher in Leeds.
He pressed for the measure to “send the strongest signal that carrying knives is unacceptable and will be punished”.
The justice secretary confirmed the Government is reviewing sentencing policy for knife crime and said that he wants a change in the law.
Mr Morris has also signed amendments to the Criminal Justice and Courts Bill, which would extend the mandatory six month minimum jail sentence for people convicted of threatening someone with a knife to any adults convicted of carrying a knife for a second time.
Young offenders aged 16-18 who are convicted for a second time would receive a minimum four month detention and training order.
Speaking after signing the amendments, Mr Morris said: “I promised Christina Edkins’s family that I would take up the issue of knife crime and would campaign for a change in the law to make sure that people caught carrying illegal knives receive the prison sentences they deserve.
“The Government has done a lot already to toughen up knife laws, including ending simple police cautions for carrying an illegal knife and introducing minimum sentences for people convicted of using one, but we need to go further to make sure that people know that carrying an illegal knife will be treated the same as carrying a gun.
“I am delighted that the justice secretary agrees with me that we need change and I look forward to voting for it in Parliament.”