* Graphic: World FX rates tmsnrt.rs/2RBWI5E LONDON, June 30 (Reuters) - The dollar was heading for its biggest monthly rise since November 2016 on Wednesday, supported by traders’ trepidation ahead of unpredictable U.S. labour data and concern over the spread of the Delta coronavirus variant. The dollar has gained about 2.5% against a basket of currencies this month, mostly in the wake of a surprisingly hawkish shift in the Federal Reserve’s rates outlook. Traders think it could move sharply in either direction if labour data this week provides clues as to the pressure on policymakers. On Wednesday, risk-sensitive and commodity-exposed currencies nursed the largest losses, after the Australian and New Zealand dollars had fallen about 0.7% against the dollar on Tuesday and the Canadian dollar had lost about 0.5%. They were steady in the European session, as were the safe-havens of the Japanese yen and the Swiss franc which held their own through Tuesday. That left the euro at $1.1900, the yen at 110.49 per dollar and the Aussie at $0.7518 - all within sight of recent milestone lows against the dollar. The U.S. dollar index, which measures the greenback against a basket of six major currencies, was steady at 92.041 after touching a one-week high of 92.194 on Tuesday. A test of the near-term dollar outlook arrives this week with U.S. labour data. Signs of strength could add to inflationary pressure on policymakers to move sooner on rate hikes, while a miss might put some padding into the timeline. Private payrolls are due later on Wednesday, but the main focus is on more comprehensive labour figures due on Friday. Economists polled by Reuters forecast private payrolls showing a gain of 600,000 in June, a slowdown from a month ago when 987,000 jobs were created. “While the dollar may be vulnerable to potential data disappointments today, we suspect that any dips in the currency would be bought ahead of the more important non-farm payroll release on Friday,” said Valentin Marinov, head of G10 FX research at Credit Agricole. The average forecast for Friday’s non-farm payrolls is for a rise of 700,000 jobs, but the variation among the 83 estimates is large, ranging from 376,000 to more than a million. Besides the looming data, a fresh spike in global coronavirus infections and in restrictive measures to contain them kept a lid on currency movements. Case counts are hitting daily records in Indonesia, lockdowns are being extended in Malaysia and expanded in Australia, while travellers from Britain are facing new restrictions as the contagious Delta variant spreads. Paul Mackel, global head of FX research at HSBC, said currency markets seemed to be in transition from closely tracking the ebb and flow of risk sentiment towards a greater sensitivity to interest rates, driving a shakeout that has lifted the dollar. “There’s been a lot of speculative build-up of short dollar positions over the last couple of months and we think that these are being washed out,” Mackel told reporters, speaking during an outlook call. Indeed, data showed the sharpest fall in the value of bets against the dollar in three months occurred last week, a boost for the greenback as the shorts buy dollars to close positions. Sterling traded flat at $1.3832. Reporting by Ritvik Carvalho; additional reporting by Tom Westbrook in Singapore; Editing by Andrew Heavens and Chizu Nomiyama Our Standards: The Thomson Reuters Trust Principles.