Italy's foreign minister Giulio Terzi has asked Britain to provide the "utmost clarity" around a failed bid to rescue a Briton and Italian in Nigeria.
He has demanded details "in the next few hours", an Italian news agency said, after accusations the UK did not inform Italy about the planned mission.
Islamist militants took Chris McManus, 28, of Oldham, and Franco Lamolinara hostage in north-west Nigeria last May.
The engineers died as Nigerian and UK forces tried to free them on Thursday.
UK Foreign Secretary William Hague and Mr Terzi are attending a meeting in Denmark. Mr Hague earlier said that the limited time available to make a decision "constrained how much we were able to consult others".
Italian President Giorgio Napolitano said it was "inexplicable" that the British government had not told Rome about the rescue attempt until it had begun.
He said the UK needed to explain why it did not inform the Italian authorities ahead of the operation.
"The way the British government has behaved is quite inexplicable. To have failed to inform or consult Italy, with regard to a military action which could have such consequences," he said.
"A clarification is needed on both the political and diplomatic levels."
UK Defence Secretary Philip Hammond said Rome had been told of intelligence behind the rescue attempt and informed "as the decision was taken to act".
Mr Hammond told the BBC News Channel that the attempted rescue had been launched after information was received that Mr McManus and Mr Lamolinara "were about to be moved - possibly executed".
He said what had subsequently happened was "very unfortunate but it's completely explicable".
"These hostages were taken, they were held at an unknown location for a very long period of time despite extensive efforts to track them down. And when a window of opportunity became available, a well-trained Nigerian force with British support, went in and tried to rescue them," he said.
"The Italian government was kept informed throughout the operation as the intelligence emerged and then as the decision was taken to act... I don't think they specifically approved it - they were informed of what was happening."
Number 10 said earlier that no official complaint had been received from the Italian government, and the UK had not made an apology.
It said the UK and Italy had been in contact ever since the men were kidnapped on 12 May, 2011.
Prime Minister David Cameron's official spokesman said: "We contacted the Italians yesterday as the operation was getting under way, but this was a very fast-moving situation.
"Our priority was to respond to the situation on the ground and to do everything we could to try and secure the safe release of the hostages."
In a statement announcing the operation and the deaths of Mr McManus and Mr Lamolinara, 48, Mr Cameron earlier said the decision to act had been taken at very short notice.
"A window of opportunity arose to try and secure their release. We also had reason to believe that their lives were under imminent and growing danger."
The BBC's diplomatic correspondent James Robbins said the Italian government tended to be in favour of negotiating in hostage situations, while Britain was absolutely against formal government negotiations.
He said it raised the question of whether Britain feared Italy would withhold its consent for the operation, although no official had conceded that.
'Window of opportunity'
News of the operation broke in a statement from the office of Italian Prime Minister Mario Monti.
It used very similar language to that used by the British side but made it clear the Italians were told the military was being used only after the operation had started.
Mr Monti chaired a meeting of a government security committee to discuss the failure of the attempt to rescue the hostages. The meeting ended after two hours without any comment being issued.
Commons Foreign Affairs Select Committee chairman Richard Ottaway said the UK was not duty-bound to tell Italy about the operation in the circumstances.
He told the BBC: "I can understand the concerns and frustrations of Italian politicians but I think they've got to accept and recognise that these are very fast-moving, delicate operations and it's not always possible to keep politicians briefed in advance of what goes on.
Mr Monti's office said he had asked Nigerian President Goodluck Jonathan to provide a "detailed reconstruction" of events as soon as possible.
Mr Cameron's spokesman said it was a Nigerian-led operation, with UK support involving the UK's elite Special Boat Service. BBC reporter Haruna Shehu Tangaza, in Sokoto, described several hours of heavy fighting.
The house where the men were being held had been under surveillance for some time.
Mr Cameron and Mr Jonathan said they believed the kidnappers had killed Mr McManus and Mr Lamolinara.
But an unnamed official from the Nigerian state security service quoted in local reports said the hostages died in the crossfire.
The Nigerian president described it as a "deeply sad and regrettable incident".
Mr Jonathan said that the men's captors had been seized and "would be made to face the full wrath of the law".
He said they were from militant Islamist group Boko Haram, which has carried out a number of attacks on police, politicians and clerics who oppose it.
Reports have emerged that a senior member of Boko Haram was captured on Tuesday, and he gave information which led forces to the house where the two construction engineers were being held.
However, on Friday, a spokesman for the group told reporters Boko Haram was not responsible for the deaths.
"We have never taken anyone hostage. We always claim responsibility for our acts," he said.
The BBC' security correspondent Gordon Corera said Boko Haram has become more violent and capable in recent years and there is a suspicion this may be a sign of the growing influence of the group al-Qaeda in the Islamic Maghreb.
Al-Qaeda in the Islamic Maghreb has a track record of kidnapping Westerners in north Africa and trying to extract ransom payments to fund its violence.
Chief of Defence Staff General Sir David Richards told BBC News that the rescue attempt had sent "a shockwave" through al-Qaeda in the Islamic Maghreb.
"We know that all their leaders are now and disarray and we're now obviously trying to track them down with our Nigerian allies," he said.
Gunmen seized Mr McManus and Mr Lamolinara in the town of Birnin Kebbi in the north of Nigeria on 12 May 2011.
They worked for Italian firm B Stabilini in the construction of a local headquarters for the Central Bank of Nigeria.
Relatives of Mr McManus released a statement saying they were "devastated" by his death but thanked those who had worked to try to free him.
"During this ordeal we have relied heavily on the support of our family and friends which has never waned and has enabled us to get through the most difficult of times," they said.
The Foreign Office advises against all travel to some areas of Nigeria and against all but essential travel to other areas, but these do not include the area where the men were kidnapped.
It says there is the threat of kidnap and terrorism across the west African country.