The dollar eased on Tuesday, inching closer to a two-month low versus the euro hit last week as investors continued to cut long positions on more disappointing U.S. economic data.

The greenback rose a little against the yen on bids from Japanese importers, but remained close to a seven-month low marked last week, leading many market players to look to what authorities in Japan could do about a firm yen.

The Australian dollar jumped more than 1 percent thanks to a rise in Chinese shares as well as buying against the yen amid wariness about Japanese yen-selling intervention.

The Wall Street Journal reported the Bank of Japan could consider taking additional steps to support the economy if the yen climbs to around 85 per U.S. dollar and stays there.

In Asian trade, the dollar rose about 0.4 percent to 87.01 yen JPY=, on buying by Japanese importers, off a seven-month low of 86.27 hit on trading platform EBS on Friday.

Traders suspect Japanese officials would not want to see the 85 level breached in a hurry, though many traders doubt Tokyo is ready to intervene at this point.

I guess the authorities will be nervous. There will be verbal intervention or they might do rate checks as they did before. But I don't think they can do actual intervention, said a trader at a Japanese financial institution.

Indeed, traders say they saw marginal yen-selling by Japanese investors.

Japanese investors' risk appetite hasn't come back. They are not ready to sell the yen yet. It's hard to expect upside for the dollar/yen, said a trader at a European bank.

Demand for the dollar waned further on Monday after the NAHB/Wells Fargo Housing Market index fell more than expected in July to its lowest level since April 2009, after a popular tax credit for homebuyers expired in April.

The report was the latest in a string of data that has flashed warnings about the state of the U.S. economy and quashed expectations of a Federal Reserve interest rate hike this year.

If Fed Chairman Ben Bernanke drops any hint of further easing at testimony on Wednesday it could push the dollar down further, some traders said.

The overall bearish setup remains intact for dollar/yen, JPMorgan said in a morning report. This follows last week's breakdown below the key 87.00/22 yen support zone while affirming the intermediate term bearish setup and a closer test of the 84.82 November 2009 cycle low.

The euro EUR= edged up 0.15 percent to $1.2963/64, not far from a two-month high of $1.3008 hit last Friday.

Traders expect the pair to trade in a $1.28-1.31 range in the coming days ahead of EU stress test results for banks and Fed chief Bernanke's testimony.

Support for the euro is seen around the previous day's low of $1.2870. Resistance comes in at Friday's high of $1.3008, while some traders say a break of that level could push it to around $1.3113, a Fibonacci retracement of its decline from last December to early June.

The results of stress tests on 91 European banks are due on Friday and there is a consensus building in the forex market that it could be positive for the euro.

Bankers and officials in Greece, Spain and Belgium joined a chorus of countries expecting their banks to pass the stress tests, but doubts linger over whether the checks are tough or transparent enough.

Some traders suspect the euro could be in for a buy on the rumour sell on fact retreat, after having risen nearly 10 percent from a four-year low, mostly shrugging off negative news on the euro zone.

It brushed aside news that Moody's had cut Ireland's debt rating and concerns that negotiations between Hungary and international lenders had broken down.

Meanwhile, the Aussie AUD=D4 rose 1.1 percent to $0.8775 and 1.4 percent to 76.38 yen AUDJPY=, helped by an upbeat mood in Chinese share markets and wariness about Japanese yen-selling intervention.

The Australian dollar quickly recovered the ground it had lost after minutes from the Reserve Bank of Australia's (RBA) July policy meeting that suggested it was unlikely to raise interest rates next month if coming inflation data showed the moderation it expected.

The currency has strong support around $0.8575-8590, where there is a 50 percent retracement of its rally this month as well as a cluster of previous lows. (Additional reporting by Anirban Nag and FX analyst Krishna Kumar in Sydney; Editing by Michael Watson)