The next date of hearing for the case is scheduled for July 10.
"The ASUS legal team is currently working with the Delhi High Court in India to resolve the Zen Mobiles and ZENFONE trademark lawsuit," ASUS said in a statement on Thursday.
"The supply of ASUS smartphones, notebooks and other products, as well as technical support and after-sales service for all ASUS products remain unchanged for all consumers," it added.
The Justice Manmohan order came on a plea filed by Telecare Network seeking to restrain ASUS from directly or indirectly selling, offering and advertising for sale mobile phones, accessories or any other related products or any other goods under the trademark ZEN, ZENFONE or identical trademarks.
The court ordered ASUS not to sell any product which is identical or deceptively similar to the trademark ZEN and ZEN Mobile.
Telecare Network said that the marks ZEN and ZENMOBILE come under the Trade Marks Act, 1999, and have been continuously and extensively used by the company in their feature phones, smartphones, tablets and accessories since 2008.
The court said: "...the triple identity test is satisfied as the defendants (ASUS) have made use of a deceptively similar/identical trademark (ZENFONE) in relation to identical goods (mobile phones) having identical trade channels."
"Consequently the defendants (ASUS) having adopted a deceptively similar mark wherein the dominant part of the defendant's mark ZENFONE is the plaintiff's (Telecare) mark ZEN, for the same product i.e. mobile phones, shows prima facie that there is a likelihood of confusion and damage to the plaintiff's goodwill," it said.
( With inputs from IANS )