US President Joe Biden has ordered US flags to be flown at half-staff over the weekend in tribute to Abe.
His Brazilian counterpart, Jair Bolsonaro, who himself survived an assassination attempt, announced three days of official mourning.
Abe was shot at twice while he was giving a speech on a street in the city of Nara on Friday morning.
The suspect, named as Tetsuya Yamagami, admitted shooting Abe with a homemade gun and said he had a grudge against a "specific organisation", police said.
