Officers from West Yorkshire Police were sent to Manchester overnight as 400 officers, many of them armed, flooded the city.
Greater Manchester Police chief constable Ian Hopkins said: “We have received tremendous support from across the police service in England and Wales and partner agencies throughout the night.
“We regularly carry out exercises to test our ability to respond to such incidents and this has ensured a very swift response from local and national agencies.
“I want to thank all members of those emergency services and other agencies who have worked tirelessly throughout the night in very difficult circumstances. Their response has been quite outstanding.
“There remains a large cordon in place around Manchester Arena and Victoria Train Station which will be in place for some time. The station will remain closed while a detailed forensic search is underway and people should plan their route to work and follow Transport for Greater Manchester for updates.
“Terrorists will attempt to disrupt our lives and create distrust and fear in our communities. We have a long history here in Greater Manchester of our communities standing together during difficult times. In the coming days we will be working very closely with community leaders to address any concerns or issues that our communities may have.
“It is important that we all continue to remain vigilant, but that we go about our daily lives. We would ask members of the public to be alert and report any suspicious activity to the police Anti-Terror Hotline, the number of which is 0800 789321 or of course ring 999.
“As people are waking up to the tragic news of what is a sad day for Greater Manchester the officers and staff of Greater Manchester Police and the other emergency services and our partners will continue to do all they can to help get us through the difficult days ahead.
“Finally I’d like to appeal to any members of the public that may have images or footage from last night that they believe can assist in our investigations, if they could upload them to Ukpoliceimageappeal.co.uk or Ukpoliceimageappeal. com, we would be very grateful.”
A spokesman for West Yorkshire Police confirmed officers had been sent to Manchester but declined to say how many.