* Safe-haven currencies rally, yen up across the board
* Swiss franc testing SNB's 1.20 per euro cap
* Putin threatens invasion to protect Russian citizens in Ukraine
SYDNEY, March 3 (Reuters) - The Japanese yen rose across the board on Monday while investors gave risk currencies such as the Australian dollar a wide berth as Ukraine mobilised for war after Russia's President Vladimir Putin declared he had the right to invade the neighbouring country.
The U.S. also threatened to isolate Russia economically in Moscow's biggest confrontation with the West since the Cold War.
The euro fell as low as 139.36 yen, from 140.56 late in New York on Friday, while both the U.S. dollar and the Australian dollar dipped to one-month lows of 101.30 yen and 90.15 yen respectively.
The safe-haven Swiss franc was also in favour, rising to its highest in over a year against the euro. It rose as far as 1.2108 francs per euro before edging back to 1.2112.
Investors were wary of testing the Swiss National Bank's commitment to defend its cap of 1.20 per euro on the franc.
Dealing risk appetite a further blow, a government survey on Saturday showed activity in China's factory sector slowed to an 8-month low in February, reinforcing signs of a modest slowdown in the world's second biggest economy.
Analysts at JPMorgan described two scenarios that could unfold from the Ukraine crisis: a possible repeat of the January 2009 interruption of natural gas supplies from Russia to Europe via Ukraine, and the less likely possibility of military conflict next door to the EU.
They said markets discounting the risk of a gas supply disruption would mark down euro against the U.S. dollar. Europe imports around 25 percent of its gas from Russia, although there are huge variations across countries, JPMorgan said.
"But unless that interruption is sustained for many weeks, Ukraine does not look like a trend driver of government bonds, swap spreads or the currency," they said.
However, should the extraordinary event of military conflict occur, they warned the euro could drop 3 to 5 U.S. cents.
The euro last traded at $1.3773 some 0.2 percent lower compared with late New York levels. The euro however was flat against other risk currencies such as the Aussie dollar.
Against the greenback, the Aussie is down about 0.3 percent at 89 U.S. cents.
There is a smattering of Asian economic data out on Monday, although probably not major enough to distract markets from developments in Ukraine.
Investors will get another look at China's manufacturing sector from a private survey, while partial indicators including inventories are due in Australia ahead of fourth-quarter gross domestic product report out on Wednesday.