Beds Police and Crime Commissioner Festus Akinbusoye tweeted: "I am just speechless."
A joint statement from the offices of Luton North MP Sarah Owen and Luton South MP Rachel Hopkins called for public order while the investigation continues.
A spokesman said: "Both of Luton’s MPs are calling for calm into response to yesterday's events which led to a tragic loss of life.
"They are in touch with Bedfordshire Police, Bedfordshire's Police and Crime Commissioner, and other affected relevant parties.
"Local people will understand that the MPs cannot comment fully while a police investigation is still ongoing, but they are encouraging anybody with any information to come forward.
"Any information will be treated in the strictest confidence."