TOKYO (Reuters) - The euro fell almost 2 percent and share prices tumbled across Asia on Monday as Greece looked set to default on its debt repayment this week, forcing Athens to impose capital controls to halt bank runs.

With the prospect of Greece being forced out of the euro in plain sight, the common currency fell as much as 1.9 percent to $1.0955, its lowest in almost a month, and last stood down 1.4 percent at $1.1007.

Against the yen, the common currency dropped more than 3 percent to 133.80 yen, a five-week low.

U.S. stock futures dived almost 2 percent at one point to hit a three-month low, and last traded down 1.6 percent.

Japan's Nikkei fell 2.1 percent while MSCI's broadest index of Asia-Pacific shares outside Japan dropped 1.4 percent.

Chinese shares were volatile and whipsawed between positive and negative territory, with the Chinese central bank's measures on Saturday to support the economy unable to calm jittery investors. [.SS]

The central bank simultaneously cut interest rates and reserve requirements for the first time since the global financial crisis in late 2008.

"It's a bit surprising that both the cut in interest rates and RRR in China have come at the same time. It shows that the Chinese policymakers feel a sense of urgency," Christopher Moltke-Leth, head of client trading at Saxo Capital Markets. "Asia is down because of a risk-off move in response to what's going on in Europe, in Greece."

Investors are flocking to safer assets, staggered by uncertainty over the future of Europe, as Greece could become the first country to leave the currency bloc after a default.

The 10-year U.S. Treasury yield fell 0.16 percentage point to 2.317 percent.

The yen, which tends to gain in times of financial stress, strengthened to a one-month high of 122.10 to the dollar.

"We are in uncharted territory and European equities, like all markets, will have a difficult time processing this," said Deutsche Bank Managing Director Nick Lawson.

"The market was not positioned for this going into the weekend and the lack of liquidity that has impacted both sovereign and corporate debt markets, as well as equity recently, will exacerbate things."

Cash-strapped Greece looks certain to miss its debt repayment to the IMF on Tuesday as Greece's European partners shut the door on extending a credit lifeline after Greece's surprise move to hold a referendum on bailout terms.

Fear of an imminent default by Greece hit Greek banks, a major buyer of Greek government bills, triggering bank runs over the weekend and forcing Prime Minister Alexis Tsipras to announce a bank holiday and capital controls.

Some investors, however, are pinning their hopes on the possibility that Greek voters will back the creditors' bailout terms in next weekend's referendum, returning Athens to the negotiating table, despite Tsipras urging a no vote.

"Right now the surprise is that the euro is not weaker. The logic may either be that the Greek government will come back to the negotiating table or that it will not survive long, if 'Yes' prevails contrary to their recommendation," said Steven Englander, Global Head of G10 FX Strategy at CitiFX in New York.

Conspicuous by its absence so far from this year's Greek drama has been contagion to other "peripheral" euro nations' government bond markets as other European banks have limited exposure to Greece.

Any speculative selling of debt of such countries as Italy, Spain and Portugal will also likely be countered by the European Central Bank, which started buying euro zone sovereign debt from the markets in March to shore up the economy.

Yet perceptions could change if investors grow more worried about the future of the currency union, including whether Greece can stay within the euro zone after default.

Some investors think Greece's attempt to abandon the austerity program - and possibly reset its economy through currency devaluation - could fuel more skepticism towards the euro project among the populace in other euro zone countries.

Gold prices gained 0.6 percent to $1,181.40 per ounce on safe-haven buying, while Brent crude oil futures fell 1.2 percent to $62.53 per barrel.