NSW man's charge upgraded to murder

A man's charges have been upgraded to murder after his alleged assault victim died in a Sydney nursing home.

Police allege the 45-year-old man pushed over a 50-year-old man in Woolloomooloo about 12.10am on April 11, leaving him in a critical condition.

The man died in a Liverpool nursing home last Wednesday.

The 45-year-old was originally charged with recklessly inflict grievous bodily harm but on Monday his charges were upgraded to murder at Central Local Court.