Alitalia are offering cheap flights between various European cities and Brazil and Argentina in March to June.
The offer includes flights from Budapest, Prague, Moscow, Berlin (and many more cities) to Rio de Janeiro and Buenos Aires.
FlyerTalkers managed to find sub-$400 flights earlier today and maybe you can too by searching flights from your nearest European city on Flugladen.de or Vayama.ie using Chrome's in-built Google Translate.
There are so many search possibilities, but as an example, we found availability for the 6th-13th May between Budapest and Rio for just under 479 euros (US $535):
We also found availability for the 30th April-14th May between Madrid and Buenos Aires (but returning to Budapest) for 473 euros (US $529):