(Updates prices, adds comments; changes byline, dateline, pvs LONDON)
* Dollar index touches lowest in more than 2-1/2 years
* Dollar falls to 4-1/2 month low against yen
* North Korea missile launch adds to U.S. politics concerns
NEW YORK, Aug 29 (Reuters) - The dollar fell to its lowest in more than 2-1/2 years against a basket of major currencies on Tuesday after a North Korea missile launch over Japan prompted repatriation flows into the yen and added to worries about U.S. politics.
The dollar index, which measures the greenback against a basket of six major currencies, touched its lowest since mid-January 2015, at 91.621, after North Korea fired a ballistic missile over northern Japan's Hokkaido island into the sea.
The missile launch in part prompted short-term speculators such as macro hedge funds to buy back yen in an unwinding of so-called carry trades, said Sireen Harajli, foreign exchange strategist at Mizuho in New York.
Carry trades occur when investors borrow a cheap currency like the yen to fund purchases of riskier and higher-yielding currencies. Harajli also said Japanese savers have been buying back the yen by selling non-yen assets in recent months, potentially given concerns about the U.S. political environment, making these savers a possible source of the yen's gains on Tuesday.
The dollar was last down 0.5 percent against the Japanese currency at 108.75 yen after falling as much as 0.9 percent earlier to a 4-1/2-month low of 108.28 yen. As recently as Friday, the dollar was at an eight-day high of 109.84 yen.
"You expect (yen) to appreciate in a risk-off event, and in this case you can compound it because the market was long dollar/yen," said Greg Anderson, global head of foreign exchange strategy at BMO Capital Markets in New York.
The dollar touched its lowest in two years against the Swiss franc, another safe-haven currency, at 0.9431 franc.
The euro gained as much as 0.8 percent, breaking past the critical $1.20 level to its highest since January 2015, to $1.2069.
Analysts said North Korea's missile launch was hurting the dollar broadly in part because the greenback has recently been considered less of a safe-haven currency given worries over the fiscal situation in Washington.
President Donald Trump stoked anxieties by threatening on Aug. 22 to shut down the government if Congress does not fund his proposed U.S.-Mexico border wall.
The lack of any mention of the euro's strength by European Central Bank President Mario Draghi at Friday's Jackson Hole conference was also seen as a tacit green signal to euro bulls, while the impact of Tropical Storm Harvey was weighing on the greenback as well, analysts said.
(Reporting by Sam Forgione; Editing by Steve Orlofsky)