* Trade war optimism fires up risk-taking
* Euro back above $1.13, but still near three-month lows
* Quiet start to the week with U.S. markets closed
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh (Updates with latest prices)
By Tommy Wilkes
LONDON, Feb 18 (Reuters) - The euro rallied and riskier currencies like the Australian dollar strengthened on Monday as optimism over a breakthrough in talks to end a U.S.-China trade war encouraged investors.
The euro has been stuck in a trading range against the dollar for several months as growing weakness in the euro zone economy offset dwindling expectations the Federal Reserve will raise U.S. interest rates again this year.
But after dropping to a three-month low on Friday, the euro has recovered, helped by improved investor sentiment as hopes rose for an end to the U.S.-China trade conflict after both sides reported progress in talks.
The dollar, the world's most liquid currency, tends to perform well during bouts of investor nervousness.
"Generally the mood is still quite positive on the outlook for trade," said Adam Cole, a currencies analyst at RBC Capital Markets, adding that he thought the "risk-on" mood would continue.
"If anything we would be running with it. You have a background of quite decent growth and a Fed that is putting rates on hold."
However, he said a better way to play the Fed's pausing of rate increases was in dollar/yen, as more Japanese investors choose not to hedge purchases of dollar-denominated assets that already earn a decent yield after 2018's U.S. rate rise.
Cole sees dollar/yen rising to 120 yen per dollar by the end of 2019 from current levels of 110.55.
The euro ticked 0.3 percent higher to as high as $1.1334 , while the dollar index, which measures the U.S. unit against a basket of rivals, slipped 0.2 percent to 96.710 in a quiet session with U.S. markets closed for a holiday.
Despite Monday's gains, traders are betting on a weaker euro in the coming months. They expect the European Central Bank to maintain its easy monetary policy against a backdrop of slow growth, tepid inflation and political uncertainty.
Commerzbank analysts said the single currency also remained vulnerable to any flare-up in a U.S.-European trade dispute.
"There would be very little to report on the euro positive side if this conflict were to escalate. The smallest economic disruptions would no doubt be damaging for the euro in the light of the fragile state of the euro zone economy," they wrote.
The Australian dollar, considered a barometer of global risk sentiment, rose 0.2 percent to as high as $0.7160, its strongest position since Feb. 6.
Sterling gained 0.3 percent to $1.2928, up from last week's one-month lows as investors awaited the outcome of Britain's divorce proceeding with the European Union, with London trying to convince Brussels to tweak its withdrawal agreement.
Emerging market currencies were mostly lower. (Editing by Mark Heinrich)