Among topics discussed by Abe and Obama will be the issue of crime committed by workers from US military base in Okinawa.
Okinawa hosts the bulk of US military forces in Japan and a number of residents resent what they see as an unfair burden in the neighbourhood.
The murder of a Japanese woman on Okinawa island had led to the arrest of a US civilian last week.
Japanese Chief Cabinet Secretary Yoshihide Suga told Reuters: "The government is fully aware of the seriousness and graveness of the recent incident in Okinawa, and considering the feelings of the people, Prime Minister Abe will seek strict measures from President Obama."
Suga had said the leaders would also discuss the global economy and other regional and global issues like terrorism, refugees, trade, cyber security and maritime security including the South China Sea dispute.
The US President is also set to make a historic visit to Hiroshima, the site of the world's first atomic bombing, on Friday.
"I want to make this a summit at which the G7 sends a clear, strong message to respond to all situations and contribute to the sustainable, strong growth of the world economy," Abe said.
Both the governments expect that the upcoming Hiroshima visit will showcase the strong bond between the former wartime rivals.