* Euro holds above $1.35, Greece remains focus before summit
* Japanese markets reopen after holiday, yen crosses edge up
* Margin traders add to euro, Aussie positions vs yen
By Charlotte Cooper
TOKYO, March 23 (Reuters) - The euro held its ground on Tuesday after rebounding from a three-week low against the dollar, helped by an improvement in risk appetite following gains in U.S. stocks but still stymied by squabbling over Greece.
One trader said there was euro buying on dips against the dollar and yen after bears failed to push it through key support at $1.3440/30 on Monday, lows in late February and early March.
Japanese markets reopened after a three-day weekend and yen crosses firmed after dipping in the previous session, while the dollar sat tight in the middle of a recent range.
"Even though we saw a sharp recovery overnight probably thanks to the passage of the healthcare reform bill in the U.S., concern over Greece and tightening, not just in China but also in India, should linger in the market," said Masafumi Yamamoto, chief FX strategist for Japan at Barclays Capital.
"There's very partial risk aversion away from the euro and some assets -- but overall risk appetite is still there."
The euro sat steady from late U.S. levels at $1.3560, after falling as far as $1.3463 on trading platform EBS on Monday, and edged up 0.2 percent to 122.40 yen.
Andrew Robinson, FX market analyst at Saxo Bank in Singapore, said euro support at $1.3440/60 was becoming important, after it held on several downward attempts. A break there could send the single currency down to about $1.3090, a 76.4% retracement of its March-November rally last year.
"At the moment we're likely to hover between $1.3440-1.3740. Even though we've had so much bad news out of the Greek situation, we still haven't broken lower and I don't think there's enough ammunition at the moment to break out of that range," he said.
That said, analysts added that continuing disagreement between Germany and its EU partners over financial support for debt-laden Greece was likely to weigh on the euro leading into a summit at the end of the week.
DOLLAR MAKES NO PROGRESS
Asian shares were broadly positive after U.S. stocks rose on Monday as the passage of a bill overhauling healthcare ended uncertainty about the reform.
The dollar index, a measure of its performance against six other currencies, eased slightly to 80.590, holding well below an eight-month high of 81.342 set in February.
The dollar gained 0.2 percent to 90.32 yen after dipping as far as 89.83 yen on Monday when Tokyo was shut.
However, it is roughly in the middle of an 88-92 yen trading range seen since mid-January, with prospects for U.S. rate hikes still distant after the Federal Reserve reiterated a pledge to keep rates low for an extended period, a stance reinforced by a non-voting Fed official on Tuesday.
Robinson at Saxo Bank said the dollar could be building a base at about 89.70/80 yen although it faced resistance from a down trend line and its 200-day moving average above 91.00.
Japanese margin traders took Monday's dip in the euro and Australian dollar against the yen as an opportunity to add to their long positions. Data showed margin traders' net long euro/yen position increased to its highest in three weeks and the long Aussie/yen position rose to a two-week high.
One manager at a margin trading house said buying could gather steam if the euro cheapened through 120 yen.
The currency market is also keeping an eye on friction between the U.S. and China over the yuan.
China's Premier Wen Jiabao was quoted by state media as saying the country would probably run a trade deficit of more than $8 billion in March, which if it happens would be the Asian giant's first monthly trade deficit since April 2004.
Many expect Beijing would want to see several sustained months of strong export growth before allowing the yuan to appreciate. (Additional reporting by Kaori Kaneko; Editing by Joseph Radford)