David Cameron has asked his national security advisor to investigate the handling of events surrounding the discovery of a viable explosive device at East Midlands airport on Friday.
Sir Peter Ricketts will examine what led to a lag of more than 10 hours between US President Barack Obama and the UK PM being told of the situation.
A No 10 spokesman said the inquiry was standard practice in such cases.
Mr Cameron has praised the police for the way they handled the incident.
But an ex-Labour minister said it was "extraordinary" that Mr Cameron had not been told immediately.
The bomb was found on a US-bound cargo plane at East Midlands airport, hidden in a printer cartridge that had been posted in the Yemeni capital, Sanaa.
It was found after a tip-off and was not picked up by initial screening.
Following the discovery, unaccompanied freight flown to the UK from Yemen and Somalia was banned.
A Downing Street spokesman confirmed that an investigation into the sequence of events following its discovery was under way and that if there were lessons to be learnt "we will learn them".
He reiterated that the prime minister and home secretary Theresa May were told at 1400 on Friday but did not dispute reporters' assertions that a minister knew at 0800 that day.
When asked why it had then taken six further hours to inform the prime minister, the spokesman said the suspicious package had undergone a "large degree of examination".
This meant, the spokesman added, that it "took some time before they - the police - were able to establish the facts".
The BBC's security correspondent Gordon Corera said questions were being asked about why it apparently took so long to inform the prime minister of the incident.
Transport Secretary Philip Hammond was told initially in the morning, because of the closure of the airport, and the home secretary was told later when it was clear the package really was suspicious, he added.
Former security minister Admiral Lord West said he found the sequence of events "quite amazing".
"I imagine there will be several 'interviews without coffee' for people as a result of this," he told the BBC.
"It is extraordinary the prime minister wasn't told almost immediately... You should know straightaway. It could have been really embarrassing for him, if something had been mentioned about this.
"I would be furious if I was him and something has slipped up in the routine and the measures that should automatically happen. I'm very surprised, I must say."