Policing and Fire Minister Nick Hurd said they wanted to provide reassurance to people living in other buildings as soon as possible.
He said: "We have discussed with the Department for Communities and Local Government, local authorities and the fire service a process whereby we seek to identify towers that might have a similar process of refurbishment, run a system of checks so that we can, as quickly as possible, give reassurance to people."
Following a meeting of the Government's Civil Contingencies Secretariat, Mr Hurd refused to be drawn on reports that ministers had been warned that building regulations were in urgent need of updating.
However he said that they were determined to establish exactly what happened.
"I am not going to comment on that at the moment," he said. "I hope people will understand that the priority of the Government at the moment is to manage the emergency response, to deal with the security, to deal with lives to be saved, lives to be rebuilt, and to make sure that we have got the support in place for this emergency response.
"That will then move into recovery phase and then we will move into a phase where we seek to answer the questions that people quite understandably have, so we really understand what happened here, what went wrong, so we don't find ourselves in this situation, because I don't think that anybody wants to go through another night like last night."
Mr Hurd said that whatever resources were needed to deal with the situation would be made available.
"Everyone I have spoken to on the frontline - the fire, the police, the ambulance services - resources have not been the issue," he said.
"People arrived very quickly in good numbers and with the right equipment to deal with an unprecedented situation last night.
"The Government is absolutely determined to make sure we are there to support the emergency and support services but also the people who have been caught up in this tragedy."