UK officials were outraged when photos appearing to show debris from the attack appeared in the New York Times.
It came after the name of bomber Salman Abedi was leaked to US media just hours after the attack.
Theresa May said she would tell Donald Trump at a Nato meeting that shared intelligence "must remain secure".
The bombing on Monday killed 22 - including children - and injured 64.
The Queen has arrived at the Royal Manchester Children's Hospital to visit some of the injured.
Greater Manchester Police hopes to resume normal intelligence relationships - a two-way flow of information - soon but is currently "furious", the BBC understands.
The force - which is leading the investigation on the ground - gives its information to National Counter-Terrorism, which then shares it across government and - because of the Five Eyes intelligence sharing agreement - with the US, Australia, Canada and New Zealand.
In total eight men are now in custody following the attack, carried out by Manchester-born Abedi, a 22-year-old from a family of Libyan origin.
It has also emerged two people who had known Abedi at college made separate calls to a hotline to warn the police about his extremist views.
Home Secretary Amber Rudd had said she was "irritated" by the disclosure of Abedi's identity against the UK's wishes and had warned Washington "it should not happen again".
However, the pictures of debris - which appear to show bloodstained fragments from the bomb and the backpack used to conceal it - were subsequently leaked to the New York Times, prompting an angry response from within Whitehall and from UK police chiefs.
BBC security correspondent Gordon Corera says UK officials believe that US law enforcement rather than the White House is the likely culprit for the leaks.
A Whitehall source described the second US leak as "on another level", and said it had caused "disbelief and astonishment" across the British government.