The euro has fallen sharply against the dollar after the anti-austerity Syriza party won the Greek general election.
The euro briefly fell as low as $1.1088 - the lowest level against the dollar in more than 11 years.
Syriza leader Alexis Tsipras has pledged to renegotiate the terms of Greece's €240bn bailout and reverse many of the austerity cuts.
But he said that he wanted negotiation, not confrontation, with Greece's international lenders.
"The new Greek government will be ready to co-operate and negotiate for the first time with our peers a just, mutually beneficial and viable solution," Mr Tsipras said.
The troika of lenders that bailed out Greece - the European Union, European Central Bank, and International Monetary Fund - imposed big budgetary cuts and restructuring in return for the money.
But Mr Tsipras said: "The troika for Greece is the thing of the past."
The euro had already been under pressure following last week's announcement of a new stimulus programme by the European Central Bank.
'Stand-off'
Greece's current bailout programme ends in February, and economists say a short term deal will be negotiated, but difficult talks lie ahead. Germany has indicated that it is not prepared to renegotiate the bailout terms, raising the prospect that Greece could end up leaving the eurozone.
"There is a danger of a prolonged stand-off with the troika as Syriza attempts to negotiate some form of official debt restructuring while not reneging on its promises to voters to cut taxes, raise government spending and increase the minimum wage," said Jonathan Loynes, chief European economist at Capital Economics.
Michael Hewson, chief market analyst at CMC Markets, said: "Tsipras's comments don't appear to leave any room for doubt as he stated that the troika and the bailouts belong to the past,.
"You can be almost certain that these negotiations will be watched carefully by the anti-austerity movements in Spain, Portugal, Italy and France to see what measures if any Greece is able to get out of EU politicians to deal with the problem of Greece's debt, and the terms of the bailout programme."
'Face value'
The UK Chancellor, George Osborne, urged all sides to "act responsibly" is any forthcoming negotiations over Greece's bailout terms. He told BBC Radio 4's Today programme that he understood why, with the Greek economy in trouble, voters were "looking for other answers".
But he warned that Syriza's election promises to spend more on public services and slow the pace of cuts were unlikely to work. "If you take at face value all the things that the new Greek government has promised, including big increases in public expenditure, I think that will be very difficult to deliver," he said.