The ambiguity allows us to understand that the subject of the sentence has ceased the activity of arguing, or that it has banned the activity among (itself and) others. Please help with a grammatical analysis which identifies the semantic distinction.
Interestingly, if you used the word "cease" you can make the distinction between your two meanings by saying:
The government ceased arguing.
The government ceased to argue.
I can't imagine a situation where you would say "the government stopped arguing" without there being some context that made the intended meaning clear. If it were a news headline it would surely have followed a previously documented spate of arguing. If you wanted to say that someone had stopped other parties from arguing, you would be specific, for example:
The teachers stopped arguing.
The teachers stopped the children arguing.
Without mentioning the children, this example does sound like the teachers are arguing among themselves, but in your example I don't think many would assume it meant the government had stopped all arguing globally because that seems impossible.