Spain's Interior Minister Jorge Fernandez Díaz has ordered a special police task force to investigate the hate tweets that targeted Catalans, but also Germans and the French.
"As well as expressing tremendous cruelty, they may constitute crimes which will have to be investigated and referred to the justice system," junior security minister Francisco Martinez told a news conference on Wednesday.
Examples of the offensive tweets, as quoted in the Spanish edition of the Huffington post, include one which said: "Lets hope that all who died in the crash were Catalans".
While another urged: "Wait, let’s not be dramatic, those on the plane were Catalans, not people".
One user tweeted: "A plane full of Catalans and Germans, crashing in France #winwinwin".
A spokesman for the Mossos d’Esquadra, the Catalan police force confirmed that the force was investigating 24 offensive tweets posted from 17 twitter profiles.
"They could constitute a hate and discrimination crime," explained Xavier Porcuna,a Mossos spokesman, speaking from Barcelona airport.
Many of the messages appeared to target Catalans, inhabitants of the culturally distinct Catalonia region and regular targets for teasing in the rest of Spain.
Most of the offending posts have now been removed.The plane took off from Barcelona, capital of Catalonia, before it crashed in southeastern France on Tuesday with the deaths of all 150 people on board.
Spain's interior ministry launched a crackdown on online hate speech in May 2014 after the killing of a ruling party politician sparked many insults online against conservative politicians.