Marketing engine Next Jump Inc agreed to stop emailing Borders Group Inc's customers while the parties hash out how to move forward in trademark infringement litigation, a lawyer for Borders said on Friday.

Next Jump, hired by Borders to operate one of its websites, consented to the request from Borders at a hearing in U.S. Bankruptcy Court, and said it would remove references to Borders' trademarks from its own website, OO.com, Borders lawyer Jeff Gleit said.

Borders, the bankrupt bookseller in the midst of winding down its operations, had sued Next Jump on Wednesday, saying it contacted Borders' customers in an attempt to steal them.

A hearing on a possible injunction is slated for Tuesday, but may be canceled if the parties can agree on terms in advance, Gleit said.

The case comes at a critical moment for Borders, which is trying to sell its trademarks, customer lists and other intellectual property.

Any infringement could cause those assets to lose value if customers are steered away from the site, the company said in court papers.

Next Jump has denied the allegations.

The facts have been significantly distorted and Next Jump has retained counsel to right the wrong we're being accused of, Meghan Messenger, a Next Jump partner, said in an email.

Borders tapped Next Jump to operate Bordersrewardsperks.com, a site established to provide rewards from third-party vendors to Borders' most loyal customers.

Next Jump allegedly emailed customers in hopes of directing traffic to OO.com, telling customers Borders' Rewards Perks is now OO.com, the lawsuit said.

The nine-count complaint includes allegations of breach of contract, trademark infringement and misappropriation of trade secrets. It also seeks punitive damages.

Borders said on Thursday the lawsuit is geared toward protecting its customers.

We take the privacy of our customers very seriously and will act to ensure that measures are taken to protect their information, Borders said.

Borders filed for bankruptcy protection after being unable to withstand the growing popularity of online booksellers as well as e-readers such as Amazon.com Inc's Kindle and Barnes & Noble Inc's Nook. The company began liquidating in July after failing to find a buyer.

The bankruptcy case is In re Borders Group Inc, U.S. Bankruptcy Court, Southern District of New York, No. 11-10614. The lawsuit is Borders Inc et al v. Next Jump Inc in the same court, No. 11-ap-02567.

(Reporting by Nick Brown, editing by Matthew Lewis)