It depends on whether you're talking about the book, or the movie.
In the book, we see absolutely nothing about the Elves when Smaug first invades Erebor. They only enter the story when the party goes to Mirkwood. In the movie, there are many, many events that the books do not mention, and this is one of them.
In the book, the only army of Elves that is seen is when Thorin escapes the Elvenking and goes to Laketown. Thranduil first heard of Thorin's arrival in Laketown from the raft-men of the Elves, who were sitting at the lower tables at feast. Indeed, when Thorin announced himself to the Master of Laketown, the Elves came forward and told the Master:
"These are prisoners of our king that have escaped, wandering vagabond dwarves that could not give any good account of themselves, sneaking through the woods and molesting our people!"
And later, we see Thranduil's reaction:
In the meanwhile the Wood-elves had gone back up the Forest River with their cargoes, and there was great excitement in the king's palace. I have never heard what happened to the chief of the guards and the butler. Nothing of course was ever said about keys or barrels while the dwarves stayed in Lake-town, and Bilbo was careful never to become invisible. Still, I daresay, more was guessed than was known, though doubtless Mr. Baggins remained a bit of a mystery. In any case the king knew now the dwarves' errand, or thought he did, and he said to himself:
"Very well! We'll see! No treasure will come back through Mirkwood without my having something to say in the matter. But I expect they will all come to a bad end, and serve them right!" He at any rate did not believe in dwarves fighting and killing dragons like Smaug, and he strongly suspected attempted burglary or something like it which shows he was a wise elf and wiser than the men of the town, though not quite right, as we shall see in the end. He sent out his spies about the shores of the lake and as far northward towards the Mountains as they would go, and waited.
Thranduil brought an army to Erebor to see what part of the treasure he could claim.