The Islamic State terror group has claimed responsibility for the Manchester suicide bombing.
A lone bomber detonated a homemade device packed with nuts and bolts in the foyer of the Manchester Arena as thousands of young people were leaving a concert by US pop star Ariana Grande on Monday night.
The attacker has not been officially named but investigators believe they know his identity.
On Tuesday, the first arrest was made in connection with the inquiry.
Greater Manchester Police said in a statement: "With regards to the ongoing investigation into last night's horrific attack at the Manchester Arena, we can confirm we have arrested a 23-year-old man in south Manchester."
One witness told how the man was detained by between six and eight plain-clothes officers in Chorlton.
As counter-terrorism agencies mounted a massive inquiry into the outrage - the worst terrorist attack since 52 innocent people were killed in the July 7 bombings in London in 2005:
:IS has frequently declared that it was behind terrorist incidents in recent years but experts have warned their claims should be treated with caution
Speaking outside Downing Street after chairing a meeting of the Government's Cobra emergency committee, Mrs May said the perpetrator had chosen the time and place of his attack deliberately to cause "maximum carnage and to kill and injure indiscriminately".
Mrs May, who later flew to Manchester to speak to police chiefs, paid tribute to emergency workers and members of the public who rushed to help.
The Prime Minister said: "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."
Mrs May said there would be "difficult days ahead" for those affected, but added: "We all - every single one of us - stand with the people of Manchester at this terrible time."
The Prime Minister said the official threat level remains at severe - meaning an attack is highly likely - but this would be assessed throughout the day.
Police were called to reports of an explosion at the Manchester Arena at 10.33pm on Monday, shortly after the end of the performance.
The massive blast sparked panic as concert-goers rushed to exit the venue, which has a capacity of 21,000.