I was just watching Return of the King and saw that one of the Dead was about to kill Aragorn with his sword & Aragorn was able to block the blow with his sword, Andúril (reforged from the shards of Narsil). I read the books a long time ago and don't quite remember how they described it. I was just wondering if the Dead would still answer to Aragorn if he did not have Andúril. Was Narsil (or a sword reforged from it) necessary to prove that you were Isildur's heir?
The Dead follow Aragorn because of who he is, not the sword he carries.
In the books there's none of this "sword-fighting with the Dead" nonsense. Aragorn doesn't even get his sword out; it's enough for him to proclaim who he is and show his banner, and the Dead follow him without question.
To that Stone the Company came and halted in the dead of night. Then Elrohir gave to Aragorn a silver horn, and he blew upon it and it seemed to those that stood near that they heard a sound of answering horns, as if it was an echo in deep caves far away. No other sound they heard, and yet they were aware of a great host gathered all about the hill on which they stood; and a chill wind like the breath of ghosts came down from the mountains. But Aragorn dismounted, and standing by the Stone he cried in a great voice:
'Oathbreakers, why have ye come?'
And a voice was heard out of the night that answered him, as if from far away:
'To fulfil our oath and have peace.'
Then Aragorn said: 'The hour is come at last. Now I go to Pelargir upon Anduin, and ye shall come after me. And when all this land is clean of the servants of Sauron, I will hold the oath fulfilled, and ye shall have peace and depart for ever. For I am Elessar, Isildur's heir of Gondor.'
And with that he bade Halbarad unfurl the great standard which he had brought; and behold! it was black, and if there was any device upon it, it was hidden in the darkness. Then there was silence, and not a whisper nor a sigh was heard again all the long night. The Company camped beside the Stone, but they slept little, because of the dread of the Shadows that hedged them round.
-- The Return of the King, Chapter 2: The Passing of the Grey Company (emphasis mine)