TOKYO—Prime Minister Shinzo Abe on Wednesday asked U.S. President Barack Obama to investigate alleged spying by the National Security Agency on the Japanese government and companies, Mr. Abe’s spokesman said.

Documents posted online by WikiLeaks last month suggested that conversations involving government officials, central bankers and Japanese companies had been secretly intercepted by the U.S. agency. In a phone conversation Wednesday morning Tokyo time, Mr. Obama expressed regret that the issue has caused trouble for Mr....