Meanwhile, Senior police chiefs in Britain reacted with anger Wednesday night after sensitive details of the Manchester Arena suicide bombing were leaked to media in the U.S.
May said she would talk to Trump at a North Atlantic Treaty Organisation summit later on Thursday about the leaks, which included the publication of photographs of the bomb site by the New York Times.
The pictures appeared in the New York Times and followed an earlier leak to U.S. media of the attacker's name.
Earlier, interior minister Amber Rudd said the bomber had recently returned from Libya.
Authorities have been investigating whether Abedi was working as part of a "network" that planned and executed the attack, according to the Times.
Initial analysis of the various elements photographed at the scene suggests that suicide bomber Salman Abedi carried "an improvised device made with forethought and care", concealed most likely within a backpack but also possibly in a vest, wrote the paper.
A source said British investigators were hunting for anyone who may have helped build the suicide bomb.
Mrs May will head to the North Atlantic Treaty Organisation meeting in Brussels and thank the Western military alliance for its support following the suicide bombing attack in Manchester.More news: ICC Champions Trophy 2017: Will Virat Kohli tinker with India's batting order?
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Britain's official terror threat level was raised to "critical", the highest level, late on Tuesday, meaning an attack was expected imminently.
Police said three suspects were arrested Wednesday in south Manchester.
But the New York Times then published photos it says were gathered by United Kingdom authorities at the scene of the attack, including the remnants of a backpack, nuts and screws, and a device identified as a "possible detonator". The elder Abedi was also later arrested.
Numerous victims were children and teenagers - with the youngest of the dead revealed to be just eight-years-old.
She continued by saying she has been thinking about her fans "non-stop", advising them that the only thing to be done now is to "choose how we live our lives from here on out".
They arrested the seventh man they believe to be connect to the attacks as they seek to stop a repeat attack from happening.
Multiple media outlets said Thursday, citing anonymous British intelligence sources, that the Greater Manchester Police would stop sharing information on their fast-developing investigation into the bombing with USA counterparts, but the United Kingdom government did not confirm that.