Prime Minister Sir Keir Starmer said: "I know the whole country is deeply shocked about what they’ve seen and what they’ve heard.
"I know I speak for everyone in the whole country in saying, our thoughts and condolences are with the victims, their families, their friends and the wider community and it’s almost impossible to imagine the grief that they’re going through, and the trauma that they’re going through.
"I do want to thank the emergency services and Merseyside Police who have had to respond to the most difficult of circumstances today."
Southport FC, whose ground is only a few streets from the scene of the attack, said it had cancelled a pre-season friendly against Morecambe FC scheduled for Tuesday "out of respect to those who have so tragically lost their lives".
It also said its club lounge would be open between 10:00 and 15:00 BST on Tuesday and specialist support staff available for anyone who wished to "gather, share their thoughts, and find support during this difficult time".
Everton Football Club and Liverpool Football Club also offered their condolences to all those affected.
Home Secretary Yvette Cooper said she was "deeply concerned" about the "very serious incident", while Southport MP Patrick Hurley added that he was "hoping for the best possible outcomes to the casualties affected".
Steve Rotheram, mayor of Liverpool City Region, has urged the public not to spread "unconfirmed speculation and false information".
Merseyside’s Police and Crime Commissioner Emily Spurrell said she was "utterly shocked and devastated" to hear of the "truly appalling" incident.
Councillor Marion Atkinson, Leader of Sefton Council, said the council was "deeply shocked and saddened at the tragic events".
“Our thoughts are with all the victims of this attack and their families," she said.
“I’d like to thank all those who responded to the incident and helped in any way they could in what must have been extremely difficult circumstances.
“We know this has caused concern and upset in the local community and while there is no immediate threat to the public we will be providing help and support in the coming days and weeks”.