The Recognition of Sakuntala is a play written in Sanskrit by the Indian poet Kalidasa. It tells the story of the Indian King, Dushyanta, and his marriage to the maiden Sakuntala. Here's a brief rundown.
According to the myth, Sakuntala is abandoned by her parents at birth and grows up in a small hermitage (sort of like a monastery) belonging to the sage Kanva. One day, while Kanva is away from the hermitage, King Dushyanta stumbles upon Sakuntala while hunting. Dushyanta falls immediately in love. He approaches Sakuntala, courts her, and then marries her. (Why waste time?)
The two are crazy happy and in love with each other, but Dushyanta has to return to the capital to fulfill his duty as king. He gives Sakuntala a ring to use as proof of their marriage when she comes to the palace to join him.
Dushyanta returns to the palace at Hastinapura. Meanwhile, an old sage stops at the hermitage where Sakuntala lives. Sakuntala is so caught up in thoughts of her new husband that she fails to offer the old man food. In retaliation, the old man curses her. (Stinky old men and their curses.) The man claims that he has caused Sakuntala's husband to forget her: the only way Dushyanta can be made to remember is if Sakuntala offers some token as proof.
Confident that she already has such a token—the ring—Sakuntala sets off for the palace. Along the way she is forced to cross a wide river. And wouldn't you know it, when she dips her hand into the water she loses the ring. She freaks out, but she presses on anyway. But true to the old man's word, Dushyanta no longer recognizes her. Sakuntala is thrown out of the palace, and her adopted father Kanva abandons her.
Sometime later a fisherman discovers the king's ring in the belly of a fish. The fisherman returns the ring to the palace, and when Dushyanta sees it, his memory of Sakuntala returns. Too late. Sakuntala is gone from the palace, and Dushyanta is engaged in war.
After Dushyanta defeats his enemies, he is offered a tour of the Hindu heavens that lasts several years. Only after his return to earth is he given the chance to reunite with Sakuntala who becomes his queen and bears him a son.
Obviously this isn't an exact copy of the Echo and Narcissus story—especially with the whole happy ending thing—but there some major similarities. The lovers meet in the forest, just like Echo and Narcissus. Dushyanta is hunting in the evening, just like Narcissus. Sure, they fall in love (not like Echo and Narcissus—at all). But after the curse is introduced Dushyanta rejects Sakuntala, just as Narcissus rejected Echo. Love and rejection go hand in hand in both of these myths. Parallel? Maybe not. Reminiscent? For sure.