Angela Merkel said Germany would do everything it could to keep the eurozone together. She also calmed fears of further bailouts for eurozone countries, saying important lessons had been learned. Greece recently won approval for a second bailout of 130bn euros ($173bn; £110bn) intended to help keep it afloat until 2014.
Germany is having to pay more than any other country for the package - angering many German citizens and politicians. Despite the measures, some analysts fear Greece might need even more help.
Asked how she saw the future for Greece, Mrs Merkel told the BBC's Newsnight programme that Athens had repeatedly said it wanted to remain within the eurozone.
“We have taken the decision to be in a currency union. This is not only a monetary decision, it is a political one. It would be catastrophic if we were to say to one of those who have decided to be with us: 'We no longer want you'." She said the eurozone would be "incredibly weakened" by a Greek exit.
She added: "It would be a huge political mistake to allow Greece to leave. That is why we will be clear with Greece, we will say: 'If you want to be part of a common currency you have to do your homework but at the same time we will always support you.'"
Asked to respond to those in Europe who feared further bailouts she said: "That is not how it is going to happen because there has been a rethink going on in Europe for some time.
"Some countries accepted the rescue package but they don't particularly relish it. They must follow conditions set out by the IMF, the ECB and the European Commission. What democratic government wants to be in that situation for the duration?
"Over the past two years in Europe, particularly in the eurozone, we have learnt a lot. We must reflect time and again, why are we together in Europe? Why are we a community that displays solidarity and bears responsibility for the others?". Mrs Merkel said Europe - and particularly the eurozone area - had "slithered into crisis" as a consequence of a global financial downturn.
She said she believed that UK Prime Minister David Cameron "was right" to have embarked on an austerity drive. "It is something that each country in Europe can do because we will all learn that no country can live beyond its means," she said.