TOKYO (Reuters) - Japan's service-sector activity returned to growth in July thanks to solid domestic demand, a survey showed on Monday, but slow overseas orders and unabated cost pressures continue to squeeze businesses.

The final au Jibun Bank Service purchasing managers' index (PMI) rose to 53.7 last month, from 49.4 in June, which was the first contractionary reading in 21-months.

While the index was back above the 50 line that separates expansion from contraction, it edged down from the flash reading of 53.9.

"The near-term outlook for the service sector appears robust, as the level of outstanding business - a bellwether for upcoming work - returned to growth territory," said Usamah Bhatti, economist at index publisher S&P Global Market Intelligence.

Respondents' 12-month future outlook also stayed strong, Bhatti added.

However, service companies' new export business fell into contraction for the first time in seven months, suggesting tepid global economic growth.

Lukewarm overseas demand has hit Japan's manufacturing sector harder, earlier surveys have indicated, coupled with higher costs of raw materials, energy and labour.

But non-manufacturers have also been hit by rising costs, according to the July service PMI data, which showed input prices rose for the 44th straight month while the prices companies charged their customers grew faster than in June.

A recent Bank of Japan (BOJ) data also showed that corporate service prices rose at the fastest speed in more than nine years.

In July, the composite PMI, which combines the manufacturing and service activities, swung back to an expansionary figure of 52.5 from 49.7 in the previous month. But managers across industries were wary of the risks of sustained inflationary pressure dragging the economy down over the coming months, Bhatti said.

The BOJ raised interest rates last week to the highest levels since 2008 in response to broadening wage hikes and service price inflation, with governor Kazuo Ueda hinting at additional hikes in coming months.

(Reporting by Kantaro Komiya; Editing by Sam Holmes)