Merkel's comments appeared to signal a further shift in Germany's position toward showing more patience even though Athens has fallen behind on the ambitious reforms and cuts it must implement in return for bailout loans.
The subtle shift comes amid calls from the International Monetary Fund to give Greece two more years to meet the agreed targets.
Merkel, who visited Athens Tuesday, has said that extending the timeframe for Greece's reforms can only be decided after a creditors' assessment expected within weeks.
Germany, Europe's largest economy, will defend the euro against the interests of international financial market players, many of whom care little for the success of Europe and are betting that the region does not have the political will to pull through, Merkel said, adding that this view was wrong.
Against the background of debates about fresh aid for struggling states like Spain, she called on her party to place more trust in Germany's euro zone peers.
"We have every reason to place our trust in others," she said, adding that France and the United States had done this for Germany after World War Two. But she said trust could only develop if countries all stick to their agreements. "We promised too much, decided too much and never stuck to it," she said, adding that this needed to change.
Euro zone officials said on Saturday that Spain could ask for financial aid from the euro zone next month and if it does the request would likely be dealt with alongside a revised loan programme for Greece and a bailout for Cyprus in one big package.
Asked in the video podcast if a European Union in which an increasing number of member states ask for financial aid was sustainable, she said: "No of course not. It would be wrong if things were to stay like this but now the markets are also testing if we will stay together."
Merkel said she was against turning the EU into a federal system like the United States: "I don't think we should overstretch ourselves."
Merkel said the awarding of the Nobel Peace Prize to the EU on Friday provided motivation to further develop the union.