Lawyer Moses Owuor, representing the hospital, contends that Opticom breached contract terms by going directly to court.
The supplier has yet to respond to the hospital's application, though Justice Peter Mulwa granted 14 days for filing.
The Nairobi Hospital has moved to the High Court seeking to stop insolvency proceedings initiated by a security systems supplier over a disputed Sh51 million debt.
In court filings, the hospital argues that Opticom (K) Limited's insolvency petition is premature as their contract requires arbitration for disputes.