Senior Labour MP Phil Goff is tipped to be the party's next leader after Helen Clark's resignation on election night.
Miss Clark said she would stand down immediately as Labour leader after the National Party won enough seats in the general election to form the next government.
Her 15 years as leader will come to an end later this month.
The leadership vote could take place within two weeks as Labour moves quickly to reorganise before the new Parliament sits for the first time before Christmas.
Dr Cullen is also standing down as deputy leader. He said on Sunday it was time to step aside as the party rebuilds but he would continue to serve in Parliament.
The political editor for Radio New Zealand says Mr Goff, the outgoing Trade Minister, is most likely to succeed Miss Clark and appears to have widespread support within the party.
He was first elected to Parliament in 1981, and served as a minister from 1984 to 1990 in the David Lange Government before losing his seat.
He was re-elected in 1993 and since 1999 has been a senior minister in the Clark Government. He comfortably retained his Auckland seat of Mt Roskill.
Speech by Clark
In a speech to supporters at the Labour Party headquarters on Saturday night, Miss Clark said she accepted the choice the public had made and accepted responsibility for the election result.
She then announced that she was standing down, to sounds of disbelief from Labour Party supporters. She told them she had done her job for the party and was stepping down to allow a fresh approach.
Miss Clark, who retained her Mt Albert electorate, earlier telephoned National leader John Key to concede the election.
She congratulated the National Party and Mr Key, saying it was a night for the winners to savour but Labour would not be going away.
Mr Goff is not saying yet whether he will stand.
He told the Result 08 programme on Radio New Zealand that Miss Clark's decision to resign came as a surprise to him, and other Labour MPs.
Party president Mike Williams also says he had no idea Miss Clark was going to resign.
Mr Williams says her resignation came as "a bolt from the blue".