Connexin said it was stopping following KCOM's offer of discussions last month.
KCOM has already deployed a gigabit-capable FTTP broadband network across the whole of Hull and holds Significant Market Power in that area.
Local MPs have previously called for firms to stop installing poles where cables already exist.
Connexin said it had "tirelessly campaigned for infrastructure sharing over the past two years".
A spokesperson said: "Our preferred method to grow our network is to access existing infrastructure.
"In the same manner that all other internet service providers, outside the Hull telecoms area, are able to do with the Openreach network, which covers the rest of the UK."
Connexin hasn’t specified how long the pause will last, but added it wanted to "show its intent to work collaboratively to the benefit of the wider community in its ongoing negotiations with KCOM".
KCOM had previously said that the infrastructure sharing trial would start in May.