(Recasts, adds details, changes byline, PVS Singapore)
* Euro inches up towards intraday peak near $1.4330
* Euro faces resistance near $1.4350/60 area
* Dollar index dips back below 2010 downward trendline
By Anirban Nag
LONDON, June 28 (Reuters) - The euro inched up on Tuesday as Asian sovereigns and macro funds bought the common currency on dips, but traders said gains could lose steam on uncertainty over whether Greece's parliament will approve austerity steps.
The common currency was up 0.3 percent at $1.4321 , not far from the day's high of $1.4330 struck in early Asian trading.
But the euro's rise is likely to stall short of resistance clustered near the $1.4350 to $1.4360 area, with market players citing talk of euro offers near $1.4320 to $1.4330.
One resistance level lies near $1.4362, the 76.4 percent retracement of the euro's drop from last week's weekly high down to Monday's $1.4102 low.
Greek parliamentary votes on austerity measures expected on Wednesday and Thursday remained the focus for investors. Approvals could give the euro a short-term boost, but if the measures are rejected, the euro could fall past its key psychological support level of $1.40.
"It is going to be very, very tight and we are getting more and more bearish of the euro given there are larger issues at stake here apart from the Greek austerity vote," said Neal Mellor, currency strategist at Bank of New York Mellon.
"The question that is in the markets' mind is 'Will an EU debt rollover plan be enough to salvage Greece?' The focus will turn to data and if there are no signs of growth, the political will to do more on Greece will be very thin."
In a move that helped soothe markets, French President Nicolas Sarkozy said on Monday that French banks had reached a draft agreement on a voluntary roll-over of maturing Greek bonds that would stretch out loans over 30 years.
But overall sentiment remained cautious as Greece's fractious lawmakers debated unpopular austerity measures that are the price of further aid from international lenders.
Without approval for the austerity measures, the European Union and International Monetary Fund say they will not disburse the fifth tranche of Greece's 110 billion euro bailout programme. Athens needs the aid to pay its bills next month and avert the euro zone's first sovereign default.
European Central Bank Executive Member Juergen Stark was cited in media reports as saying that Greece will receive further financial help only if it sticks to implementing austerity measures and that there were no alternate plans if the reforms were not approved.
Talk of a 'Plan B' in the event of a failure to pass the Greek austerity measures has been doing the rounds, offering some support to the currency. Three euro zone sources told Reuters on Monday that European Union officials were working on a contingency plan for Greece in case its parliament rejects the austerity programme and the country cannot receive the next instalment of EU/IMF emergency loans.
NEAR-TERM VIEW
Speculators have been cutting bullish bets on the euro, but Washington's own fiscal problems and steady buying of the single currency by Asian central banks have been lending it vital support.
"The market seems to be taking its cues not so much from whether Greece's problems will be solved or not, but on whether or not there might be a default in the very near future," said Makoto Noji, senior bond and currency strategist for SMBC Nikko Securities in Tokyo.
Even if Greece averts a default in the near term, its fiscal problems are unlikely to be resolved, Noji said.
"But if there is no near-term default, hedge funds that trimmed positions in risky assets could put them back on," Noji said.
The dollar index was down 0.26 percent at 75.195, back below a downward trendline drawn off peaks hit in June 2010 and January 2011 that now lies near 75.55.
A clear breach of that resistance and a mid-June high of 76.015 could set the dollar index up for further gains. Above the mid-June peak, the next major peak on charts is at 76.366, a high hit in late May.
The dollar dipped 0.1 percent against the yen to 80.81 yen . Stiff technical resistance near 81 yen as well as dollar-selling by Japanese exporters, helped weigh on the dollar, market players said. (Additional reporting by Masayuki Kitano; Editing by Hugh Lawson)