* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
LONDON, July 2 (Reuters) - The dollar edged lower on Tuesday as optimism from a weekend trade truce between the United States and China faded, while the Aussie gained after the central bank cut interest rates as expected but signaled a more balanced outlook.
Risky assets struggled to gain momentum after Monday's relief rally with weak manufacturing surveys pointing to global economic headwinds.
JPMorgans gauge of global manufacturing fell to its weakest in almost seven years, showing contraction for the second month in a row, while Morgan Stanleys surveys showed world manufacturing shrinking for the first time since 2016.
"The impact of the optimism around the G20 meeting has faded and we are near levels where we were before the meeting," said Kamal Sharma, director of G10 FX strategy at Bank of America Merill Lynch in London.
Against a basket of its rivals, the dollar was 0.1% lower at 96.75 and not far from a three-month low of 95.84 hit last week with traders firmly of the view the Fed will cut interest rates at least three times by the end of the year.
However, the dollar's losses were relatively tiny in comparison with Monday's 0.6% bounce when global risky assets rallied on relief of waning tensions between Washington and China.
"Bigger hurdles lie ahead this week, notably ADP tomorrow and NFP on Friday," said Kenneth Broux, a currency strategist at Societe Generale in London, referring to jobs data later this week.
The global investor spotlight will move to U.S. non-farm payrolls data due on Friday, which economists expect to have risen by 160,000 in June, compared with a 75,000 increase in May.
The euro got a brief boost after a media report that European Central Bank policymakers are in no rush to cut interest rates at a July policy meeting.
The single currency edged as much as 0.25% higher to the day's highs at $1.1322 before retracing some of its rise to stand 0.1% up on the day at $1.1300.
Though central bank officials are divided on the timing of the next policy move from the central bank, market gauges of interest rates have increased the odds of an ECB rate cut later this month, thanks to a global drop in bond yields.
With volatility subdued - for example, an index measuring broad currency moves is near a record low - and central banks in easing mode, markets are ultra sensitive to any slight tweak in policy settings.
The Australian dollar was the sole spot of strength in the global currency markets as it bounced 0.3% after a central bank rate cut decision offered few clues about future easing.
The central bank lowered interest rates by 25 basis points to a record low of 1.00%, matching economists' expectations. It said it would lower rates again "if needed", a phrase some analysts took to mean an additional rate cut was less likely than previously thought.
Traders attributed the currency's bounce to heavy short positions built up in the Aussie ahead of the decision. Latest positioning data showed short bets at a six-month high.
(Reporting by Saikat Chatterjee Editing by Andrew Heavens and Andrew Cawthorne)