FOREX-Dollar treads water after disappointing U.S. jobs data

* Downbeat U.S. jobs data gives dollar bulls no reason to cheer

* Investors cautious ahead of Greece's referendum on Sunday

* U.S. markets closed on Friday for Independence Day

By Lisa Twaronite

TOKYO, July 3 (Reuters) - The dollar stuck around the previous session's levels in Asian trading on Friday, as disappointing U.S. employment data and caution ahead of Greece's referendum on bailout conditions kept the market mood subdued.

Against its Japanese counterpart, the dollar was buying 123.08 yen, nearly flat on the day and up from a session low of 122.81 yen. The greenback was holding well above a five-week low of 121.93 hit on Tuesday.

The euro edged up about 0.1 percent to 136.55 yen, and also gained about 0.1 percent against its U.S. counterpart, to $1.1093.

Volume was relatively low, which market participants said stemmed from Friday's closure of U.S. markets, in observance of Independence Day.

Caution also reigned ahead of Greece's Sunday referendum on an international bailout deal that could ultimately determine whether it stays in the euro zone.

The International Monetary Fund warned on Thursday that Greece would need an extension of its European Union loans and a potentially large debt writeoff if it cannot implement economic reforms and its growth slows.

"From our point of view in Japan, it is very difficult to determine what the Greek people are hoping for, so it is difficult to predict the outcome of the vote," said Ayako Sera, senior market economist at Sumitomo Mitsui Trust Bank in Tokyo.

"Until the outcome of the referendum is known next week, investors here are hesitant to take currency positions," she said.

On Thursday, the U.S. payrolls report showed employers hired 223,000 workers last month, fewer than the 230,000 increase forecast by economists polled by Reuters. The government also downgraded its reading on April and May job growth.

Investors had been hoping that solid improvement in the labour market would reinforce expectations that the U.S. Federal Reserve will raise interest rates as early as September, but payrolls data was not as robust as many expected.

While the downbeat report gave dollar bulls little to cheer about, it was not gloomy enough to quash expectations for the Fed's tightening later this year.

"We do not think that the report will significantly shift opinion within the Fed about timing of the first rate hike, which we continue to expect in September," strategists at Barclays (LSE: BARC.L - news) wrote in a note.

The Australian dollar fell to its lowest level since mid-April after the country's retail sales rose 0.3 percent in May, short of the 0.5 percent increase forecast. April was downwardly revised to a fall of 0.1 percent, the first monthly decline in 11 months.

The Aussie slid as far as $0.7566, reaching a low not seen since mid-April. It last stood at $0.7586, down 0.6 percent on the day and about 0.9 percent on the week. Key support is still seen at $0.7534, a six-year trough plumbed in early April. (Editing by Richard Borsuk)