(Corrects 7th paragraph to show the euro's 3-1/2-month low at ... $1.4218 ... not $1.4318)
* Australian and UK markets reopen after long weekend
* But activity likely slow with limited Tokyo flows
* Brighter U.S. econ outlook in the new year supports dollar
By Satomi Noguchi
TOKYO, Dec 29 (Reuters) - The dollar held firm against the yen and the euro on Tuesday as investors looked ahead to the greenback's direction in the new year after a rally this month.
Activity is expected to pick up somewhat with Australia and UK markets reopening after holidays, but traders said flows from Japanese companies will likely be limited as many of these companies are entering year-end holidays.
The dollar has risen broadly in recent weeks on optimism the U.S. economy may be poised for better growth in 2010.
Traders said upward pressure on long-term Treasury yields is providing support to the dollar against the yen after U.S. government bonds traded lower the previous day and pushed the benchmark 10-year note yield to its highest in nearly five months.
"Given the fact that upward pressure remains on Treasury yields, dollar/yen still has the potential to reach as high as mid-92 within the year," said Toshihiko Sakai, a manager for forex trading at Mitsubishi UFJ Trust Bank.
The dollar was steady from late New York trade at 91.69 yen, within a reach of a two-month high of 91.88 set last week.
The euro was little changed at $1.4376 after having rebounded above $1.44 in holiday-thinned trade late last week from a 3-1/2-month low of $1.4218 hit a week ago.
Some traders said the dollar may struggle to rise further after speculators have finished covering their short dollar positions.
Data on Monday showed speculators were long in the U.S. currency for the first time since May, ending 32 straight weeks of short dollar positions.
Factors to watch on Tuesday that could move the dollar include Standard & Poor's/Case-Shiller home price index for October and U.S. consumer confidence for December. (Editing by Chris Gallagher)