German Chancellor Angela Merkel said if the Pope feels he is too weak to carry out his duties, that "must be respected."
The new Pope may be elected in time for the start of the Holy Week on March 24, according to Vatican spokesman Federico Lombardi.
Pope Benedict will honour his official commitments and public engagements until February 28, the date of his resignation, according to Vatican spokesman Federico Lombardi.
The Archbishop of Canterbury said he learned of the Pope's resignation with a heavy heart but complete understanding, according to Reuters.
David Cameron said: "I send my best wishes to Pope Benedict following his announcement today. He has worked tirelessly to strengthen Britain's relations with the Holy See.
"His visit to Britain in 2010 is remembered with great respect and affection. He will be missed as a spiritual leader to millions."
Pope Benedict XVI made his decision to resign "in the last few months", according to Vatican spokesman Federico Lombardi.
Vatican spokesman Federico Lombardi said the Pope's resignation was his own "personal decision" without any outside pressure.
Vatican spokesman Federico Lombardi said the Pope's resignation was not due to any specific illness but advancing age.
He added that the Pope may have wanted to resign now in order to avoid the rush of Easter engagements.