* Dollar index nudged off 2-week highs
* U.S. yields fall as post-G20 optimism ebbs, British yields slide
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh (Adds details and quotes, updates prices)
TOKYO, July 3 (Reuters) - The dollar struggled for traction on Wednesday as fading hopes for any near-term Sino-U.S. trade deal revived safe-haven demand and drove U.S. bond yields to their lowest levels since late 2016.
U.S. yields also tracked a decline in their British counterparts to 2-1/2-year lows on dovish-sounding comments from Bank of England Governor Mark Carney, which in turn weighed on the pound.
The dollar index against a basket of six major currencies was a shade lower at 96.697 after pulling back from 96.875 scaled on Tuesday, its highest since June 20.
The pound was steady at $1.2592 after shedding 0.35% the previous day, when it touched a two-week trough of $1.2584.
The BoE's Carney said on Tuesday that a global trade war and a no-deal Brexit were growing risks to Britain's economy, which might need more help to cope with a downturn, prompting investors to increase their bets on central bank easing.
The dollar lost 0.3% to 107.580 yen, having been nudged off a 12-day high of 108.535 scaled at the start of the week.
"The dollar fell below 108.00 yen again in light of BoE Governor Carney's dovish comments, which helped depress global bond yields," said Shinichiro Kadota, senior strategist at Barclays in Tokyo.
"Yields declined as the BoE, up until now, was seen as the only central bank which was not as dovish as others."
The euro was little changed at $1.1291 following a volatile session on Tuesday, when it swung between a low of $1.1275 and a high of $1.1322.
The common currency had received a lift after a media report that European Central Bank policymakers are in no rush to cut interest rates at a July policy meeting. But it later slipped after IMF Managing Director Christine Lagarde, perceived as a policy dove, was nominated as the next ECB president.
"It will be difficult for Lagarde to emulate the eye-catching policy steps which (current ECB President Mario) Draghi implemented," said Daisuke Karakama, chief market economist at Mizuho Bank.
But the euro zone's requirements will remain the same -it needs lower yields and a weaker currency - and the ECB is unlikely to undergo a dramatic change in policy under Lagarde, he added.
The Australian dollar was flat at $0.6991 after gaining about 0.4% the previous day. The Aussie had advanced after the Reserve Bank of Australia cut interest rates but offered a more balanced outlook.
The 10-year U.S. Treasury yield extended an overnight fall and brushed 1.948%, its lowest since November 2016.
At the G20 summit in Japan last weekend, Washington and Beijing agreed to restart trade talks after U.S. President Donald Trump offered concessions.
But investors were wary about the chances of a resolution to the year-long trade war between the world's two biggest economies, especially given the recent breakdown in talks in May and Trump's comments that any deal would have to be tilted in favour of the United States.
Sentiment was also dented by Washington's threat of tariffs on $4 billion of additional European Union goods in a long-running dispute over aircraft subsidies. (Reporting by Shinichi Saoshiro Editing by Shri Navaratnam & Kim Coghill)