Facebook Inc. said it could be on the hook for $3 billion to $5 billion in additional taxes as a result of an Internal Revenue Service investigation into how the social network transferred assets overseas.

The company said in a quarterly filing Thursday that the IRS had issued a “statutory notice of deficiency” a day earlier saying Facebook owes more taxes for 2010. The July 27 notice came the same day that Facebook said second-quarter profit nearly tripled to $2.06 billion.