Voldemort, once known as Tom Riddle the heir of Salazar Slytherin is seen inside the chamber of secrets as a product of his first Horcrux i.e., his diary as Tom Riddle. We see a younger version of Voldemort as Riddle in the chamber, so it suggests that he is able to transform into some kind of unconventional form. Also, he was able to cast spells as it was shown when he casts ‘flagrante’ to spell out ‘Tom Marvolo Riddle’, which is then disentangled into ‘I Am Lord Voldemort’. So why didn’t he kill Harry at that moment?
Harry showed his loyalty towards Dumbledore, so when he got poisoned by Basilisk, Fawkes appears to help him. Meanwhile, Riddle laugh’s at the Phoenix, and when Harry kills the Basilisk Riddle was just watching and shouting, expecting the poison to do its work. So why he waited for Harry to destroy the Horcrux? Why he didn’t kill him in the first place?
To get the answer we need to consider Voldemort’s history. Tom Riddle is a much younger version of his present self as Voldemort, doesn’t processes all of the memories that his present self version has. That means he doesn’t really know about Harry. So, by talking to Ginny Weasley, Riddle gets to know why Harry is so famous. Additionally, he wanted to get aquatint exactly how his present self was defeated by Harry.
For the latter reason, it seems logical to set forth Basilisk on Harry because if something goes wrong it would be Basilisk’s defeat, as Riddle wouldn’t want Harry to vanquish him twice. Riddle’s arrogance and conceit got better of him as when Fawkes came he didn’t do anything as he was convinced that Basilisk’s poison will kill Harry and therefore Riddle missed the chance to kill him.