* Dollar falls after biggest weekly drop in more than a month
* Yen edges lower though short positions decline
* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
LONDON, March 26 (Reuters) - The euro vaulted above the $1.24 line to the day's highs and relatively high-yielding currencies, including the Australian dollar, gained on Monday as stocks recovered, indicating investor appetite returned after Friday's brief sell-off.
But the dollar held close to a 16-month low against the Japanese yen as broader markets remained wary about the greenback's outlook against the backdrop of concerns over a possible trade war.
"The Fed's statement last week, if anything, signals a more bullish outlook for the dollar, but we are seeing renewed weakness so this may be indicative of some structural rebalancing flows," said Richard Falkenhall, a senior FX strategist at SEB.
With positioning against the dollar at a one-year high, according to CFTC data, and the greenback recording its biggest weekly drop in a month against a basket of currencies last week, some investors prepared for a bounce.
But cracks widened, with the dollar plumbing to a 16-month low against the Japanese yen to 104.56 earlier and was trading slightly above that low at 105.11 yen.
Against the euro, the dollar was trading at a 2-1/2 week low of $1.2417, with the latest comments from Jens Weidmann, Germany's likely candidate to become the European Central Bank's next president, also offering some support.
Weidmann said market expectations of a rate hike towards the middle of next year were "not completely unrealistic", a view shared by the broader market, although some expect a rate hike by the first quarter of 2019.
Still, while the ECB is hinting at raising interest rates, the Federal Reserve is already in the midst of its rate hiking cycle, with bond markets expecting more than 100 basis points in hikes over the next year, according to Reuters data.
Global markets were shaken last week after U.S. President Donald Trump moved to impose tariffs on Chinese goods, edging the world's two largest economies closer to a trade war, but latest reports indicated a slightly more selective stance.
The United States asked China in a letter last week to cut the tariff on U.S. autos, buy more U.S.-made semiconductors and give U.S. firms greater access to the Chinese financial sector, the Wall Street Journal reported on Monday, citing unnamed sources.
U.S. stock futures were up 1.4 percent in London trade after major U.S indices fell sharply on Friday.
"Risk sentiment remains cautious and we remain bearish on the dollar's outlook in the absence of any fundamental changes despite the rate differential factor supporting the greenback," said Manuel Oliveri, an FX strategist at Credit Agricole in London.
Against a broad basket of its rivals, the dollar edged 0.3 percent lower after last week's 0.8 percent fall.
The dollar's strength against the yen was also due to Japanese factors such as growing views that a political scandal in Tokyo could deepen, with a figure in a cronyism controversy surrounding Prime Minister Shinzo Abe due to testify in parliament on Tuesday.
The prime minister's "Abenomics" economic measures have been a factor in pulling the yen down over the past few years to the benefit of Japanese exporters. Any event that leads to a decline in his support ratings is seen weakening his ability to keep Abenomics in place.
"With worries about the United States and China locking horns on trade issues and Japan's parliamentary testimony coming up on Tuesday, few participants are willing to buy the dollar," said Yukio Ishizuki, senior currency strategist at Daiwa Securities.
According to calculations by Reuters and Commodity Futures Trading Commission data released on Friday, speculators' net short positioning on the yen shrank rapidly to roughly 22,000 contracts in the latest week, the smallest since November 2016, from a net short position of about 79,500 contracts.
The Australian dollar added 0.6 percent to $0.7749 and the New Zealand dollar gained nearly 1 percent to $0.7297, in a further sign that risk aversion was fading from the markets for now.
(Reporting by Saikat Chatterjee; Additional reporting by Shinichi Saoshiro in TOKYO; editing by David Stamp and Louise Heavens)