* Easing of Treasury yields dulls demand for dollars
* Speculation of more ECB action keeps pressure on euro
* Euro near lowest since January 2013 vs Swiss franc (Adds dollar dip, quotes, latest prices, changes byline and dateline; previous LONDON)
NEW YORK, Aug 26 (Reuters) - The dollar softened on Tuesday after a run of gains while the battered euro continued to struggle on expectations of soft inflation data and more monetary easing.
The dollar index, a basket of currencies traded against the greenback, was down 0.07 percent in early New York trading after touching a 2014 high of 82.613.
Against the yen, the dollar was off 0.15 percent at 103.91 yen.
The euro was at $1.3198 after touching a low of $1.3178 in Asian trade, its weakest since Sept. 9.
"After a couple of sessions of solid gains for the dollar, it's not unlikely to see a little profit-taking, a little consolidation," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington. "Yields are moving lower and that's weighing on the dollar."
Prices for U.S. Treasuries were up on Tuesday, with the benchmark 10-year note yielding 2.373 percent after opening at a yield of 2.384 percent.
Currency prices were only mildly affected by data showing orders for long-lasting U.S. manufactured goods had posted their biggest gain on record in July on strong international demand for aircraft.
"The durable goods orders were a slight miss," Esiner said.
For the euro, weak German economic figures and the resignation of the French government following a row over fiscal policy added to the bearish mix.
The euro zone shared currency was trading at 1.2086 Swiss francs, having fallen to 1.2072 on Monday, its lowest since early January 2013 on trading platform EBS.
Its drop could test the Swiss National Bank's three-year-old pledge to cap the franc at 1.20 per euro.
Investors betting on more euro weakness are waiting for euro zone inflation data on Friday. Analysts polled by Reuters expect annual inflation to have slowed to 0.3 percent in August from 0.4 percent in July. That would be well below the European Central Bank's danger zone of 1.0 percent and its target of just under 2.0 percent.
Late on Friday, in stronger language than he has used in the past, ECB President Mario Draghi said the bank was prepared to respond with all its "available" tools should inflation drop further.
Those comments have triggered speculation that the ECB may be prepared to ease policy further, driving bond yields lower.
In contrast to Draghi, Federal Reserve Chair Janet Yellen on Friday acknowledged the concerns of some Fed officials about the sustained level of monetary policy stimulus, even as she stressed the need to move cautiously on raising benchmark interest rates. (Editing by James Dalgleish)