SHANGHAI, Oct 27 (Reuters) - Fierce rivals Shein and PDD Holdings-owned Temu have applied to end their legal fights with each other in the U.S., documents show, marking a truce even as a global market share battle between the low-price online platforms heats up.

Joint declarations were filed to courts in Chicago and Boston by lawyers representing the companies and their subsidiaries, requesting that two legal cases be dismissed "without prejudice" by their judges.

The filings did not contain details on why they had decided to drop their complaints or whether any settlement had been made. Neither firm immediately responded to a request for comment on the filings on Friday.

Shein's lawsuit against Temu, filed last December in the U.S. District Court for the Northern District of Illinois, alleged that Temu told social media influencers to make disparaging remarks about the fast-fashion retailer, and tricked customers into downloading the Temu app using "imposter" social media accounts.

In July, Temu filed its own lawsuit in Boston federal court, accusing Shein of violating U.S. antitrust law in its dealings with clothing manufacturers.

Temu's complaint alleged Shein "forces manufacturers to sign loyalty oaths certifying that they will not do business with Temu."

In previous statements, both firms denied any wrongdoing in the cases.

The two companies have shaken up the global retailing landscape with an ultra-fast fashion, low-price shopping model.

Shein, founded in China, and valued at $66 billion, sells fast fashion at rock bottom prices, including dresses priced at $10 and bike shorts for around $5. The company produces clothing, mainly in China, that is sold online in the U.S., Europe and Asia.

Temu, whose parent company PDD Holdings also owns Chinese shopping platform Pinduoduo, similarly sells low-priced clothing but is equally well known for stocking cheap headphones and home appliances.

According to a note from HSBC analysts published this week, Temu is targeting $16 billion in gross merchandising volume (GMV) in 2023, versus consensus estimates of $11 billion. (Reporting by Casey Hall; Editing by Christian Schmollinger)