Speaking in Downing Street after she chaired an emergency meeting of police and security officials, Mrs May said “the spirit of Britain will never be broken” by terrorism.
The Prime Minister said police and intelligence agencies already know the identity of the lone attacker who detonated a suicide bomb, killing 22 people and wounding 59, but were not confirming his name at this stage.
Investigators are working to establish whether the terrorist had been part of a wider network or had received support from accomplices.
“Our thoughts and prayers are with the victims and the families and friends of all those affected,” Mrs May said.
“It is now beyond doubt that the people of Manchester and of this country have fallen victim to a callous terrorist attack, an attack that targeted some of the youngest people in our society with cold calculation.
“This was among the worst terrorist incidents we have ever experienced in the United Kingdom.
“And although it is not the first time Manchester has suffered in this way, it is the worst attack the city has experienced and the worst-ever to hit the north of England.”
The Prime Minister said the terrorist had detonated his bomb “near one of the exits” to the Manchester Arena, where the singer Ariana Grande had just finished a concert, “deliberately choosing the time and place to cause maximum carnage and to kill and injure indiscriminately”.
“All acts of terrorism are cowardly attacks on innocent people but this attack stands out for its appalling, sickening cowardice - deliberately targeting innocent defenceless children and young people who should have been enjoying one of the most memorable nights of their lives,” the Prime Minister said.
Many of the 59 wounded who are being treated in eight hospitals across Manchester have “life-threatening” injuries, and many are children, she added. “We struggle to comprehend the warped and twisted mind that sees a room packed with young children not as a scene to cherish but as an opportunity for carnage.”
Mrs May expressed the country’s gratitude towards the emergency services for their “great courage”.
“They acted in accordance with the plans they have in place and the exercises they conduct to test those plans and they performed with the utmost professionalism,” she said. “Four hundred police officers were involved in the operation through the night and many paramedics, doctors, and nurses have worked valiantly amid traumatic and terrible scenes to save lives and care for the wounded.”
The Prime Minister confirmed that following a review of intelligence, the UK terror threat level will remain at Severe, meaning a terror attack is “highly likely”.
She asked witnesses who might have any relevant information to “think of those people who are experiencing unimaginable worry” due to missing loved ones and pass it on to Greater Manchester Police.
Mrs May will travel to Manchester later to meet with Chief Constable Ian Hopkins, Greater Manchester mayor Andy Burnham, and members of the emergency services. A second emergency Cobra meeting will take place later today.
“At terrible moments like these, it is customary for leaders, politicians, and others to condemn the perpetrators and declare that the terrorists will not win.
“But the fact we have been here before and the fact we need to say this again does not make it any less true.
“For as so often while we experienced the worst of humanity in Manchester last night, we also saw the best.
“The cowardice of the attacker met the bravery of the emergency services and the people of Manchester.”
The Prime Minister called on people hold on to images of those who helped the victims, rather than of “senseless slaughter”.
“For they are the images that embody the spirit of Manchester and the spirit of Britain - a spirit that through years of conflict and terrorism has never been broken and will never be broken,” she said.
“And today, let us remember those who died and let us celebrate those who helped - safe in the knowledge that the terrorists will never win and our values, our country, and our way of life will always prevail.”