* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
* Dollar slips, erasing gains made after solid PMI readings
* European stock markets buoyed by strong German, French data
* Oil rises on Saudi pledge to cut exports
LONDON, July 25 (Reuters) - The dollar sagged to a more than one-year low and European stocks climbed on Tuesday, as investors bet that subdued U.S. inflation and political strains in Washington would limit Federal Reserve interest rate moves for the rest of the year.
The Fed starts a two-day meeting later in the day to discuss its monetary stance and the timing of its long-awaited balance sheet reduction, a plan most likely to be detailed in September.
There is a growing sense that it will want to tread carefully, and markets were reflecting that with cautious risk appetite in Europe, where sentiment also got a boost from "euphoric" German economic data and news that Greece was tapping capital markets for the first time since 2014.
Strength among commodity firms and banking stocks as well as a string of solid updates also boosted European shares as the euro, the pound and the region's other main currencies took advantage of the soft dollar.
The U.S. currency was stuck at its lowest since June 2016 to add to a near 4 percent drop over the last month and more than 8 percent this year.
The political troubles of President Donald Trumps White House continue to mount, with investigations into his pre-election links to Russia deepening. There is also growing anxiety about the United States hitting another debt ceiling in October with few moves to potentially offset that.
"We may seem some consolidation here from the dollar but fundamentally our bearish view on it remains," UniCredit Global Head of FX Strategy Vasileios Gkionakis said.
"What the Fed says tomorrow is the million dollar question... but the risk is that they sound a bit more cautious after the fourth consecutive downside surprise in inflation."
The debt ceiling issue has started to cause problems at Treasury bill auctions and the three-month T-bill yield rose above the 6-month equivalent late Monday to account for the outside risk of a technical default.
Against the yen, the dollar eased to 111 yen having slipped as low as 110.625 yen, its lowest since mid-June, the previous day. Analysts see it sliding under 110 if the Fed shows signs of serious concern this week.
The greenback was also lower against the euro again at $1.1652, having hit a near two-year low earlier in the week of $1.1656.
The single currency got a further boost as German business morale hit new high, with firms "euphoric" according to the Munich based Ifo economic institute that compiles the data from 7,000 of them in Europe's largest economy.
"Hardly anything seems to be able to hit the German economy," Ifo economist Klaus Wohlrabe added, saying German business was experienced in managing the impact of exchange rate moves following the euro's sharp rise.
Greek government borrowing costs meanwhile hovered near their lowest level since 2010, as the country sought to sell its first longer-dated bond in three years.
Some five years since European Central Bank Mario Draghi pledged to do "whatever it takes" to preserve the euro, the debt sale by the euro zone's weakest economy is the clearest sign yet of the bloc's recovery from a crippling debt crisis.
It also spurred demand for other low-rated debt, with bonds of Portugal, Italy and Spain outperforming those in powerhouse Germany.
The gap between Italian and German 10-year bond yields narrowed to its smallest since December 2016 at 153 basis points.
In commodities, oil prices extended their recovery on a pledge by leading OPEC producer Saudi Arabia to cut exports in August to help reduce the global crude glut. Haliburton Co's executive chairman also said the U.S. shale drilling boom would probably ease next year.
U.S. crude jumped 0.6 percent to $46.63 a barrel, after closing up 1.25 percent on Monday.
Global benchmark Brent added 0.55 percent to $48.87, extending Monday's 1.1 percent rise.
The moderation in the dollar helped gold pull up, with the precious metal edging up almost 0.1 percent to $1,255.87 an ounce. (Reporting by Marc Jones; editing by John Stonestreet)