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, which left 22 dead.
Theresa May said she would tell Donald Trump at a Nato meeting that shared intelligence “must remain secure”.
The US’s acting ambassador to the UK “unequivocally condemned” the leaks in a BBC radio interview.
“These leaks were reprehensible, deeply distressing,” Lewis Lukens said.
“We have had communications at the highest level of our government … we are determined to identify these leaks and to stop them.”
Meanwhile, the Queen has been to the Royal Manchester Children’s Hospital visiting some of the injured as well as members of the emergency services.
While there she paid tribute to Manchester and the “extraordinary” way the city had responded to Monday’s attack at an Ariana Grande concert, in which 116 people were also injured.
In total eight men are now in custody following the bombing carried out by Manchester-born Abedi, a 22-year-old from a family of Libyan origin.
The arrests have been “significant” while searches of premises have also yielded items “important to the investigation”, Greater Manchester Police said.
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.
A Whitehall source said Abedi was one of a “pool” of former subjects of interest whose risk remained “subject to review” by the security service and its partners.