Adds details throughout, recasts paragraph 1 with details on valuation

June 22 (Reuters) - Uber-backed Lime, an electric bike and scooter network operator, is seeking a valuation of up to $1.66 billion in its U.S. IPO, becoming the latest firm looking to tap public markets.

The company and some selling shareholders are looking to sell about 6.96 million shares in total, priced between $24 and $26 apiece.

The market for new listings has rebounded from volatility linked to the Iran war, with many hopeful issuers pushing ahead with their plans to go public as strong equity markets and blockbuster IPOs shore up investor appetite.

San Francisco-based Lime, which provides short-term rentals of electric bikes and scooters, filed for its public offering last month.

The firm was founded in 2017 and is helmed by former Uber executive Wayne Ting. Lime operates in about 230 cities across 29 countries, according to a filing with the U.S. Securities and Exchange Commission.

Lime has applied to list on the Nasdaq under the ticker symbol "LIME." Goldman Sachs, J.P. Morgan and Jefferies are among the underwriters for the offering.