By Tetsushi Kajimoto and Izumi Nakagawa

TOKYO (Reuters) - Confidence at Japanese manufacturers held steady in July but was expected to worsen to zero in the next three months, a Reuters poll found, as Britain's vote to exit the European Union further clouded the outlook for Japan's export-reliant economy.

The Reuters Tankan, which tracks the Bank of Japan's quarterly tankan survey, also found the service sector's mood fell in July to levels last seen in April 2013 when the BOJ embarked on massive monetary stimulus to reflate the economy.

The monthly poll of 534 big and mid-sized firms taken July 1-15, of which 266 responded, offered an early glimpse of Japanese business sentiment in the wake of the Brexit vote, which briefly prompted a sharp yen gain to below 100 yen versus the dollar <JPY=>.

The Reuters Tankan sentiment index for manufacturers was unchanged at 3 in July and was seen worsening to zero in October, dragged down by exporters of cars, electronics, steel and chemicals.

The sentiment indexes subtract the percentage of companies saying conditions are poor from those saying conditions are good. A positive number means optimists outnumber pessimists.

The service-sector index fell to 15 from 17 in June, and was seen unchanged in October, reflecting weak domestic demand.

Bleak business sentiment should add to calls for policymakers to do more to revive a flagging economy, with the government eyeing a stimulus package of 10 trillion yen ($94.62 billion) or more and the Bank of Japan under pressure to ease policy further.

"We cannot see the future, given the effects of a rapid yen gain due to Britain's vote to leave EU," a manager at a chemicals firm said in the survey, which companies answer anonymously.

"Capital expenditures are being put off because of uncertainty over Europe caused by Britain's exit from the EU, as well as a slowdown in China's economy, and currency situations," a machinery maker said.

While the safe-haven yen has fallen to around 105 since last week as global risk aversion abated, manufacturers reported concerns over another possible spike in the yen because of uncertainty over the global economic outlook.

Last week Prime Minister Shinzo Abe ordered compilation of an economic stimulus package by the end of this month to respond to weak private consumption and investment, and external risks. Speculation also lingers that the BOJ may ease again at its July 28-29 policy review.

($1 = 105.6900 yen)

(Reporting by Tetsushi Kajimoto; Editing by Eric Meijer)