Abe met with British Prime Minister Theresa May on Friday, assuring her that he "continued to trust the UK economy after separation from the European Union," he told a press conference in London on Saturday.
But he warned that "all the stakeholders, including investors from countries outside the region" needed to have "clear future prospects" in a post-Brexit Britain.
More than 1,000 Japanese companies do business in Britain, employing some 140,000 local people, and Japan's direct investment in the country has topped 10 trillion yen ($96 billion) to date.
Japan has already warned that businesses with their European headquarters in the UK may decide to transfer their head-office function to continental Europe if EU laws cease to be applicable in the UK after its withdrawal.
Japan's major automakers have so far backed the British economy with Toyota announcing a £240 million investment in a car assembly plant while Nissan gave the green light to new investments at its plant in northeast England.
The announcements raised questions about what assurances they had been offered by the British government.
EU president Donald Tusk said Friday that Britain must first settle the divorce issues of "people, money and Ireland" before any talks on a post-Brexit trade deal.
Abe said he was worried about Britain suddenly leaving the bloc.
"Maintaining an open Europe is a matter of concern to the world," he said. "If the rules change overnight, there will be a concern about a possible confusion arising.
"I highly regard that the UK attaches importance to a smooth and transparent process including setting a transition period," he told the London press conference.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)