Kitching joined Harrogate on an initial month`s loan in January and after impressing for the promotion-chasing outfit, will remain at the CNG Stadium for the rest of the campaign.
The centre-back was on the scoresheet for Town last weekend, helping them defeat Leamington 3-1.
Town currently sit in second place, two points behind leaders Salford City and are vying for promotion.
Speaking about the extension, Leeds academy manager Adam Underwood told his club`s official website: We’ve had really positive feedback on Liam’s performances at Harrogate and extending his loan until the end of the season is the right thing for his development at this time.
"He is ready for the challenge of senior football, we will continue to monitor his progress closely and assess his next step during pre-season".