* Euro falls more than 1 pct vs dollar
* Euro/pound hits lowest level since late July
* Political uncertainty seen hurting Italian banks
By Hideyuki Sano
TOKYO, Dec 5 (Reuters) - The euro tumbled in early Asian trade on Monday after Italian Prime Minister Matteo Renzi said he would resign after conceding defeat in a referendum over his plan to reform the constitution.
The euro dropped 1.3 percent to $1.0505, falling below its 1 1/2-year low of $1.0518 touched late last month, and testing its key support levels where the currency has managed to rebound in the past couple of years.
A break below its 2015 March low of $1.0457 would send the currency to its lowest level since early 2003, opening a way for a test of $1, or parity against the dollar, a scenario which many market players now see as a real possibility.
Renzi's departure looks set to boost political uncertainty in the euro zone's third largest economy, as his Democratic Party (PD) is running neck-and-neck with the anti-euro 5-star Movement in the opinion polls.
It also came at a bad time for Italy's fragile banking system, as Monte dei Paschi di Siena, the country's third biggest but ailing lender, needs to raise 5 billion euros by year end to avert the risk of being wound up.
"The "No" vote was priced in to a certain extent in advance. So I do not expect a freefall in the euro in the near term," said Minori Uchida, chief currency analyst at the Bank of Tokyo-Mitsubishi .
"But in the long run, this will delay progress in Italy's efforts to get rid of banks' bad debt and is likely to widen the yield spread of German Bunts and the Italian bonds," he added.
The referendum outcome could be taken as another sign of rising anti-establishment sentiment in the core of Europe, potentially eroding investor confidence in the euro ahead of elections in France and Germany next year.
One comfort for investors, however, was that Austrian voters roundly rejected on Sunday a candidate vying to become the first freely elected far-right head of state in Europe since World War Two, halting at least temporarily the wave of populism sweeping Western democracies.
Against the yen, the common currency fell more than 1.0 percent to 118.70 yen while it also shed more than 0.7 percent to 0.8315 British pound, its lowest level since late July.
The yen rose to 112.87 per dollar and last stood at 113.20 per dollar, up 0.3 percent from late U.S. levels and bouncing back further from its 9-1/2-month low of 114.83 touched last week.
The dollar softened on Friday as investors took profits from its recent gains following solid, but not spectacular, U.S. non-farm payrolls data.
Some investors are also starting to see that market realignments after the U.S. elections - including a rally in U.S. stocks and the dollar and sell-off in U.S. bonds and emerging market currencies -- may have run their course at least for now.
DoubleLine Capital Chief Executive Jeffrey Gundlach, known as the "Bond King" on Wall Street, said financial markets could reverse their solid momentum at the latest by U.S. President-elect Donald Trump's Jan. 20 inauguration.
Data from U.S. financial watchdog also showed on Friday that speculators' net long position on the dollar rose to their highest since mid-January. They also turned net short on the Japanese yen for the first time since last December. (Reporting by Hideyukia Sano; Editing by Chris Reese and Eric Meijer)