British Foreign Secretary Liz Truss said the UK "stands with our Japanese friends at this difficult time."
French President Emmanuel Macron said he was "deeply shocked" by the heinous attack on Abe.
"Thoughts to the family and loved ones of a great Prime Minister. France stands alongside the Japanese people," he added.
Russian Foreign Ministry spokeswoman Maria Zakharova, in a statement, said: "We are convinced that those who planned and committed this monstrous crime will bear the due measure of responsibility for this act of terrorism, which cannot be justified," ministry's spokeswoman said in a statement.