Counter terror police chiefs said the leak undermined their investigation and victims' and witnesses' confidence.
A Whitehall source added: "We are furious. This is completely unacceptable."
Greater Manchester Mayor Andy Burnham said he had raised the leaks with the US ambassador.
Earlier UK Home Secretary Amber Rudd said she was irritated with the US for releasing information about bomber Salman Abedi.
Ms Rudd said she had told Washington "it should not happen again".
But the New York Times then published photos it says were gathered by UK 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 paper said the alleged evidence suggested "a powerful, high-velocity charge, and a bomb in which its shrapnel was carefully and evenly packed".
The photos were subsequently published in the UK media.
"These images leaked from inside the US system will be distressing for victims, their families and the wider public," the Whitehall source added.
"The issue is being raised at every relevant level by the British authorities with their US counterparts."
The UK's National Police Chiefs' Council said it valued its relationships with "trusted intelligence, law enforcement and security partners around the world", saying this allowed "privileged and sensitive information" to be shared in the fight against terrorism.
But it added: "When that trust is breached it undermines these relationships, and undermines our investigations and the confidence of victims, witnesses and their families.
"This damage is even greater when it involves unauthorised disclosure of potential evidence in the middle of a major counter terrorism investigation."
Mr Burnham told Newsnight a decision had been taken to adopt a "cautious approach" to making information public, "and yet the first reports were coming seemingly out of the United States".
"But it worries me greatly and in fact I made known my concerns about it to the US ambassador," he said, adding: "The British police and security services need to be in the lead when this is a live investigation here."
Labour's Yvette Cooper, who chaired the influential Commons Home Affairs Committee before the general election campaign started, tweeted: "V troubled by US leaking intelligence UK has given them in middle of live investigation where public safety at risk. What is going on?"
Monday night's attack at Manchester Arena killed 22 people - including children - and injured 64.
Information about the bomber's identity first emerged in the US - with American TV networks CBS and NBC naming Abedi as the suspect.
On Wednesday morning Ms Rudd was asked whether she would be looking at how information sharing may have resulted in the premature release of details the British police and security services had not wanted in the public domain.
"Yes, quite frankly," the home secretary told BBC Radio 4's Today programme.
"The British police have been very clear they want to control the flow of information in order to protect operational integrity - the element of surprise - so it is irritating if it gets released from other sources, and I've been very clear with our friends that that should not happen again."
Pressed on whether the Americans had compromised the investigation, she said: "I wouldn't go that far, but I can say they are perfectly clear about the situation and that it shouldn't happen again."
The UK government and police have reacted with anger after a US newspaper published photos apparently showing the scene of the Manchester bomb attack.