The National Counter Terrorism Policing body said the breach of trust caused great "damage" and "undermines our investigations".
"Our family is devastated and words can not express how we feel at losing our darling Eilidh", the statement, released via the GMP, said.
The force has reportedly stopped sharing intelligence relating to the attack with the USA government after concerns that American intelligence officers were continuing to leak confidential details of the investigation to the American media. Prime Minister Theresa May is expected to confront President Trump over the leaks when they meet in Brussels, Belgium, Thursday at the North Atlantic Treaty Organisation summit.
A spokeswoman for Rudd declined to clarify her comments.
The suspected bomber grew up in Manchester's southern suburbs and once attended Salford University there.
Many of the Libyan expatriates clustered in Manchester, creating one of the largest Libyan communities outside Libya, according to Nazir Afzal, who until 2015 was the chief prosecutor for northwest England, based in the city.
New details about Abedi emerged Wednesday, including that he had been known to intelligence services, Rudd told the BBC.
After the bombing, Grande suspended her Dangerous Woman tour and canceled several shows in Europe.
But President Trump critics, including some U.S. intelligence officials, call his complaint ironic after he gave highly sensitive information about a foreign country's covert operation against ISIS to senior Russian officials in a White House meeting this month.
Other European security agencies have also been criticized for failing to keep track of potential attackers.
There were plenty of warning signs before Salman Abedi unleashed carnage at Manchester Arena.
"We have evidence that he is involved in Daesh (Islamic State) with his brother".
Soldiers were seen at the Houses of Parliament, May's Downing Street residence and at the London police headquarters at New Scotland Yard. They said such groups "work in cult-like secrecy, often via the internet; few of us will ever meet anyone with these sort of sympathies". France's interior minister Gerard Collomb said British investigators told French officials they suspect Abedi may have also recently traveled to Syria, France's BFMTV and the New York Times reported.
Under normal circumstances, he said, Abedi may have been able to travel to the United States because he was from Britain, a visa-waiver country, but he would have been subjected to a background check via the USA government's Electronic System for Travel Authorization, or ESTA.
A European security official said, "having a US leak when the situation has developed in the U.K.is nothing new". The official spoke on condition of anonymity because the information hadn't been cleared for public release.