Government sources said British construction worker Chris McManus, 28, and Italian engineer Franco Lamolinara, 47, were killed by members of the militant Islamic group Boko Haram as the rescue operation started Thursday, Britain's Guardian reported.
It was unclear how close the 20-person British force was when the men were killed in Sokoto by hostage-takers who officials said retaliated for the rescue attempt, The Guardian said.
The two men were working for an Italian building company when gunmen kidnapped them in Birnin Kebbi city May 12.
Some Italian lawmakers said the Italian government had not been told of the rescue operation.
"We must shed full light on the reasons why the British government did not inform our own," said Massimo D'Alema, president of the parliamentary committee for the security of the republic.
Rosa Calipari, a member of the Italian Parliament, questioned why Italian authorities and intelligence officers in Nigeria were not involved in the decision to proceed with the operation.
"It would seem that despite the presence of an Italian who had been in the hands of kidnappers for a long time, our country was told only after the blitz," Calipari said.
British officials said Italian security personnel had been told of the operation as it began but a conversation between Prime Minister David Cameron and Italian counterpart Mario Monti was delayed because Monti was traveling by aircraft as the operation ended.