The conclave of cardinals, which begins on April 18, will have to weigh up a wide range of issues, particularly given the outpouring of affection that John Paul inspired.
Australian Cardinal, George Pell, who is in Rome, says the next pontiff would follow the conservative line taken by John Paul II.
A nine day period of mourning has begun following the funeral of the Polish-born pontiff.
He was laid to rest in Saint Peter’s basilica after an elaborate and emotional service attended by about one million people and watched by countless others around the world.
The pope was buried in the crypt close to the spot said to contain the remains of Peter, the apostle chosen by Jesus Christ to found his church almost 2,000 years ago.
About 300,000 mourners thronged in and around Saint Peter’s Square, where the pope’s body lay in a plain wooden coffin during the mass attended by the political and religious leaders of more than half the world’s nations.
An estimated 700,000 other pilgrims filled surrounding streets to watch the ceremony on giant video screens.
World leaders, including UN Secretary General Kofi Annan and US President George W. Bush, were in attendance.
Mr Bush later told reporters on the plane taking him back to Washington that attending the funeral was “one of the highlights of my presidency.”
He said he had been particularly moved by the final moments of the ceremony, when “the plain-looking casket (was) carried and held up for the seal to be seen and then the sun pouring down.”
An open red-bound New Testament was placed on top of the coffin, its pages riffling in the wind.
In Jerusalem, Israeli public radio reported that during the pope’s funeral President Moshe Katsav shook the hand of Syrian President Bashar al-Assad and also spoke in Persian with Khatami.
Mr Assad later took the initiative to shake Mr Katsav’s hand a second time, the radio said.
The Vatican says the crypt, which is normally open to visitors, will be closed until Monday.