Home Secretary Theresa May said that events in Cumbria were "very serious and tragic".
She said: "Our thoughts are with the families and friends of the victims of these shootings.
"It's a terrible incident that has taken place in Cumbria today but I would like to pay tribute to the way in which the police and emergency services have worked very closely together to deal with this incident."
She said she would not comment on the details of the police investigation but will make a statement in the House of Commons.
Ms May added: "In the meantime, I want the people of Cumbria to know that they have my support and are in my thoughts."
Earlier in the Commons, David Cameron pledged to do everything possible to help communities "shattered" by the killing spree.
Updating the Commons at the start of Prime Minister's Questions, he said: "The House will be alarmed and shocked by the events unfolding in Cumbria today.
"The Government will do everything it possibly can to help the local community and those affected and to keep the House informed.
"When lives and communities are suddenly shattered in this way, our thoughts should be with all those caught up in these tragic events, especially the families and friends of those killed or injured."