German Chancellor Angela Merkel has told the BBC it would be a huge political mistake if debt-stricken Greece was allowed to leave the euro.
In an exclusive Newsnight interview, she 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.
And she applauded the UK government's austerity programme, saying "no country can live beyond its means".
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.
"It has major weaknesses but it is trying to overcome them, be they in the administration or the competitiveness of their business community. It is going to be a long and arduous road," she said.
"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.
"People all over the world would ask: 'Who will be next?'"
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.'"
Mrs Merkel said democracies had grown used to spending more than they earned, and had to be more careful to live within their means.
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.
"It is a very tense situation right now," she said.
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.
"All European countries have understood this lesson. But we in the eurozone are convinced that together, we are so much stronger."
Asked if she could envisage the UK playing a bigger role in Europe than it does now, she said: "Britain plays a very important role in Europe.
"Britain has a lot of common ground with Germany on how we see the future of free global trade, we all benefit from it.
"At the end of the day the British have to decide for themselves to what extent they wish to be part of Europe.
"It is a discussion that we have seen unfortunately taking a painful turn on the [recently agreed] fiscal compact but Britain needs to know that we in Germany want a strong Britain in the EU, we always have and we always will."
She added: "In Germany we will try to see that there is less red tape, more political decisions and more transparency. I think that we are at one on this with Britain."
Watch the full interview with Angela Merkel on Newsnight on Monday 26 March 2012 at 10.30pm on BBC Two, then afterwards on the BBC iPlayer and Newsnight website.