At the launch of the UK Independence Party's manifesto on Thursday, deputy leader Suzanne Evans said May "must bear some responsibility" for the terror attack in Manchester this week due to policing budget cuts.
Abedi, was born and raised in Manchester, reportedly spent three weeks with his family in Libya shortly before the attack.
Prime Minister Theresa May is expected to raise the issue of the leaks with President Donald Trump in Brussels later.
British police and security services were also upset that Abedi's name was apparently leaked by US officials and published while police in Britain were withholding his name.
The magazine also reports that British police informed their German counterparts Abedi had received paramilitary training in Syria.
British officials are particularly angry that photos detailing evidence about the bomb used in the attack were published in the New York Times.
Greater Manchester Police have released a statement condemning US intelligence leaks on the Manchester bombing on behalf of the National Counter-Terrorism Policing units.
It said it valued its relationships with "trusted intelligence, law enforcement and security partners around the world", and this allowed "privileged and sensitive information" to be shared in the fight against terrorism.
The name of the bomber, Salman Abedi, was disclosed to US media just as raids were underway both in Manchester and in Libya, where the bomber's father lives.
"This damage is even greater when it involves unauthorized disclosure of potential evidence in the middle of a major counterterrorism investigation".
A British official says police in Manchester will stop sharing information about their bombing investigation with the USA until they get a guarantee that there will be no more leaks to the news media.
Late Wednesday night police announced on Twitter that searches in the city's Moss Side area were ongoing and reported that a controlled explosion had taken place. Those include Abedi's two brothers, Hashim and Ismail, as well as his father, Ramadan Abedi.
"The alleged leaks coming out of government agencies are deeply troubling", Trump said in a statement released after he arrived in Brussels for a North Atlantic Treaty Organisation summit, also attended by May. The elder Abedi denied that he was part of the militant group and told the Associated Press (AP) that his son was not involved in the concert bombing and had no connection to militants.
Grande had kept a low profile since the blast.
Meanwhile, Wednesday at Boca Raton Airport Grande returned to her home with family by private jet.