By Sam Forgione

NEW YORK (Reuters) - The U.S. dollar slipped against the British pound and the euro on Tuesday as the market took a breather and potential profit-taking after a brutal two-day selloff in sterling and the euro sparked by Britain's vote to leave the European Union.

Analysts said traders took some profits on short bets against sterling and the euro in the wake of the British referendum. The rebound was slight compared to the two-day plunge following the vote, however, with sterling still down more than 10 percent from its closing price on June 23.

"It’s more kind of technical in nature, people taking profits," said David Gilmore, partner at FX Analytics in Essex, Connecticut. "I don’t think anyone is making the case for being long sterling."

Sterling was last up 0.9 percent against the greenback at $1.3346 <GBP=D4>, regaining some ground after hitting a 31-year low of $1.3122 on Monday. Sterling hit a session high of $1.3421 earlier. The euro was last up 0.3 percent against the dollar at $1.1053 after hitting a 3-1/2 month low of $1.0909 on Friday.

The pound's two-day slide on Friday and Monday was the biggest in the post-1973 floating exchange rate era and came as UK bank shares lost a third of their value in two trading sessions.

The dollar index <.DXY>, which measures the greenback against a basket of six major currencies, was last down 0.3 percent at 96.220, after posting its strongest two-day gain since Sept. 2008 on Friday and Monday as traders sought the greenback for its relative safety.

The riskier, higher-yielding Australian dollar <AUD=D4> was last up 0.6 percent at $0.7369 on the greater calm in markets and risk appetite, while the dollar was last up 0.8 percent against the safe-haven yen at 102.79 yen <JPY=>. The dollar hit a more than three-week high against the Swiss franc <CHF=>, another perceived safe-haven, of 0.9837 franc.

Despite the temporary relief in currency markets, uncertainty remained over the fall-out from the Brexit vote.

European Central Bank President Mario Draghi told EU leaders at a summit on Tuesday he agreed with private economists that predict that euro zone growth will be reduced by roughly 0.3 to 0.5 percent cumulatively over the next three years due to the Brexit vote, an EU official said.

(Additional reporting by Anirban Nag in London; Editing by Chizu Nomiyama and Andrew Hay)