By Sam Forgione

NEW YORK (Reuters) - The U.S. dollar slipped against the euro and sterling for a second straight day on Wednesday on potential profit-taking and a rebound in risk appetite stemming from reduced concerns surrounding Britain's vote to exit the European Union.

Sterling <GBP=D4>, which suffered its biggest one-day fall in modern history on Friday, was last up 0.7 percent against the greenback at $1.3434. In earlier U.S. trading, sterling hit a session high of $1.3534, marking a more than four-cent rebound from a 31-year low of $1.3122 touched on Monday.

Sterling declined more than 17 cents overall in the two days following the Brexit vote.

"There’s some element of profit-taking," said Alan Ruskin, global head of FX strategy at Deutsche Bank in New York, in reference to traders repurchasing sterling and the euro after betting against or "shorting" the currencies. "It’s just a pullback, I think, from the first, most negative reactions" to the Brexit vote, he said.

The euro was last up 0.4 percent against the dollar at $1.1105 <EUR=>, rebounding further from a 3-1/2-month low of $1.0909 on Friday. Analysts said traders were relieved by the prospect of prolonged negotiations among European policymakers before the UK's divorce from the EU.

The dollar index, which measures the greenback against a basket of six other major currencies, was last down 0.5 percent at 95.764 <.DXY> after hitting a more than 3-1/2-month high of 96.705 on Monday.

Riskier commodity-linked currencies such as the Australian and New Zealand dollars gained, with the Aussie last up 0.7 percent at $0.7440 <AUD=D4> and the kiwi <NZD=D4> up 1.1 percent at $0.7119.

The EU's 27 member states, excluding Britain, met Wednesday in Brussels following Tuesday's summit with the British prime minister, to discuss how to respond to the Brexit vote.

Traders were also likely calmed by the fact that Britain had not started the formal process of quitting the EU by invoking Article 50 of the Lisbon Treaty, said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.

Analysts said uncertainty remained and sterling had further room to fall. The dollar, which sank against the safe-haven yen after the Brexit vote, was last down just 0.2 percent at 102.54 yen <JPY=>.

The dollar was last down 0.2 percent against the Swiss franc at 0.9796 franc <CHF=>.

(Additional reporting by Jemima Kelly in London; Editing by James Dalgleish and Alistair Bell)