The vote is set for September 20th. It's the first time in 6 years that candidates will campaign for the party leadership, as Abe was re-elected uncontested last time.
He is seeking a third consecutive term as party president in a race that effectively decides who leads Japan.
Abe said on Sunday he's ready to lead efforts to prepare the country for the future and that the election centers on how this should be done.
His only opponent so far, Ishiba, says he hopes to have a good debate on key issues such as social security and economic policy.
The winner will be decided by ballots cast by party members in the Diet, as well as rank-and-file supporters.
It's been long speculated that Abe would be running again and Ishiba announced his intention earlier this month. This will be a rematch of the 2012 race, when Abe beat Ishiba in a close runoff.
How will the next leader be decided?
The winner will be whoever is able to secure a majority of 810 votes. Half of these are from individual LDP Diet members. The other half is awarded based on the percentage of votes the candidates garner from thousands of local party members.
The campaign officially kicks off early next month, but there are already some early indicators. Among Diet lawmakers, about 70% have already voiced their support for Abe.
But Ishiba could have an edge among local members. In 2012, he garnered more votes from rank-and file voters than Abe. He has also served as LDP Secretary General and Local Revitalization minister so he has strong grassroots connections.
It's expected Abe's campaign will emphasize continuity and stability by focusing on what he's achieved in his past two terms as LDP President. He'll likely say the economy has improved due to his "Abenomics" policies. He's also expected to stress his diplomatic agenda, which he says has strengthened links with the international community.
Meanwhile, Ishiba has stressed the need for change to restore public trust in the government. Recently, there have been a number of government scandals, including allegations that officials gave Abe's friend preferential treatment to open a veterinary school. While Ishiba hasn't explicitly accused Abe, he has made indirect references to the scandal.