* Euro eases, but up from previous day's 3-month low
* Political uncertainty in Greece seen as euro negative
* Market positioning may support euro -analyst
* Dlr/yen bids may emerge around Y79.50 and below -trader
SINGAPORE, May 8 (Reuters) - The euro eased on Tuesday but stayed above the previous day's three-month low, with market positioning seen offering the currency some support even as worries over political uncertainty in Greece clouded its outlook.
The single currency dipped 0.1 percent from late U.S. trade on Monday to $1.3043, but stayed well above Monday's trough near $1.2955, its lowest level since late January.
The euro had initially come under pressure on Monday after the outcome of elections in Greece and France cast doubt on the ability to push through austerity plans regarded as key to tackling the euro zone debt crisis.
"This seems to me like a pretty serious situation," said Satoshi Okagawa, senior global markets analyst at Sumitomo Mitsui Banking Corp. in Singapore, referring to the election outcomes and political uncertainty in Greece.
The single currency's downside may be limited, however, since many market players have already taken bearish bets on it, Okagawa said, adding that other analysts he spoke to recently held a similar view.
"Everyone says the euro has nowhere to go but down based on economic fundamentals, but they also say that market players are already betting in that direction," he said.
Data from the U.S. Commodity Futures Trading Commission shows that currency speculators still held a relatively large net short position in the euro in the week ended May 1.
That suggests the euro could gain a lift if short-covering kicks in.
"It might be hard to sell the euro aggressively, and the risk may be toward the upside," Okagawa said.
One cloud that hangs over the euro is political uncertainty in Greece.
A first attempt to form a new Greek government collapsed in less than a day on Monday, following an election that left gaping questions over the country's ability to avert bankruptcy and stay in the euro.
Three Greek finance ministry officials told Reuters the country might run out of cash by the end of June if it does not have a government in place to negotiate the next installment of EU/IMF aid and projected state revenues fall short.
Against the yen, the euro edged up 0.1 percent to 104.40 yen , having climbed from a three-month low near 103.24 yen hit on Monday on trading platform EBS.
The dollar rose 0.2 percent against the yen to 80.03 yen . The dollar is likely to attract buying interest at levels below 79.50 yen or so, said an FX sales trader for a major Japanese bank in Tokyo.