(Reuters) -- The dollar fell Tuesday as easing fears about the threat posed to the euro zone by Greece diminished the U.S. currency's safe-haven appeal, while Asian shares crept higher following a rally on Wall Street.

The euro sat near its highest level in a week after an orderly auction of Greek default insurance prompted traders to scale back their bets against the single currency.

There has been an unwinding of short euro positions because the reasons for holding those positions have not materialized, said Douglas Borthwick, managing director of FX broker Faros Trading in Stamford, Conn.

MSCI's broadest index of Asia Pacific shares outside Japan <.MIAPJ0000PUS> inched 0.1 percent higher, led by a 0.4 percent gain for South Korean stocks <.KS11> as shares in Samsung Electronics (005930.KS) touched an all-time high.

The Asian tech sector was boosted by Apple Inc's (AAPL.O) announcement of a $10 billion annual dividend and share buy-back, a move that lifted the S&P 500 <.SPX> to within 10 percent of its all-time closing high.

A steady stream of data pointing to a recovery in the U.S. economy and massive liquidity injections from major central banks have combined to drive a rally in share markets since late last year. The S&P 500 has risen nearly 12 percent so far in 2012 and the MSCI Asia ex-Japan is up more than 13 percent.

That, in turn, has stemmed the flow of money seeking safety in assets such as U.S. Treasuries and the dollar.

The U.S. currency was down 0.4 percent on Tuesday against a basket of major peers <.DXY>, while the euro held steady around $1.3235.  Tokyo markets were closed for a holiday.

(Reporting by Alex Richardson; Editing by Ron Popeski)