Observers say the pair are unlikely to win
Harald Tom Nesvik, a member of the right-wing Party for Progress, said that he had nominated the two world leaders for fighting terrorism and promoting world peace.
"The background for my nomination is their decisive action against terrorism, something I believe in the future will be the greatest threat to peace," he told the Associated Press news agency.
"Unfortunately, sometimes... you have to use force to secure peace."
'Unlikely'
However observers say that the pair are unlikely to win the award because Bishop Gunnar Staalsett, one of five members of the secretive Nobel committee, has spoken out against the air strikes in Afghanistan.
Although the committee does not divulge the names of those nominated, those who put names forward may reveal their choices.
Mr Nevik has the ability to nominate because he is a member of a national legislature.
Nominations for the prize were due in to the Nobel awards committee by 1 February, however as long as they are posted before the date they can still be accepted.
Prestigious
The Nobel Peace prize, named after Swedish industrialist Alfred Nobel, has been awarded in a glittering Oslo ceremony every October since 1901.
Last year a total of 126 individuals or organisations were nominated for the prestigious award, the winner of which receives just under $1 million.
It is expected that the events of 11 September will prove influential in this year's award, and some observers are predicting nominations for former New York Mayor Rudy Giuliani and architect Guy Tozzoli, who designed the World Trade Center.
Last year the Nobel Peace Prize was won by the United Nations and its Secretary General, Kofi Annan.