(Reuters) - The euro and sterling fell Tuesday after rating agency Moody's warned it may cut its triple-A ratings of France, Britain and Austria while downgrading several euro zone countries, including Italy.

The euro dipped around 40 pips after the Moody's announcement to as low as $1.3145 at one point, and last stood at $1.3162, down 0.2 percent from late U.S. trade on Monday.

The sterling took a hit as Moody's became the first major rating agency to put a negative outlook on Britain's triple-A rating and fell 0.3 percent to $1.5727.

The Moody's decision on euro zone sovereign ratings follows a similar one by Standard & Poor's last month, when France and Austria lost their triple-A status while Italy, Spain, Portugal, Cyprus, Malta, Slovakia and Slovenia were downgraded.

Still, the announcement from Moody's may provide enough impetus for the euro to decline further in the near-term, said a trader for a European bank in Singapore.

I think the euro will trade lower towards $1.3080, the trader said, adding that there could be a flush out of long euro positions taken recently by short-term speculators.

The single currency rose as high as around $1.3284 on Monday after Greece's parliament approved an austerity bill, bringing the country a step closer to securing a second EU/IMF bailout and soothing investor jitters about the possibility of a messy default.

Greece, however, still faces some hurdles before it can secure such aid.

The European Union has given the fragile ruling coalition of Prime Minister Lucas Papademos until Wednesday, when euro zone finance ministers are expected to meet, to specify how 325 million euros of the 3.3 billion euros demanded in budget savings will be achieved.

By the same deadline, Greek political leaders must give a written commitment to implement the terms of the deal.

While the situation in Greece is heading in the right direction, the euro is unlikely to make significant gains versus the dollar based on factors such as the economic outlook, said Koji Fukaya, chief currency analyst at Credit Suisse in Tokyo.

I think it will be hard for the euro to test the upside and try for levels such as $1.34 or $1.35, Fukaya said, adding that

there was not much reason to expect the euro to rise aside from the potential for short-covering.

The dollar eased 0.1 percent versus the yen to 77.53 yen.

The yen may take cues from the Bank of Japan's policy decision due later on Tuesday. Pressure has been mounting on the BOJ to set a Fed-style explicit inflation target, and the central bank may respond on Tuesday by using stronger language to describe its commitment to beating deflation.

(Editing by Sugita Katyal)