June 1 (Reuters) - U.S. President Joe Biden met with major infant formula manufacturers on Wednesday, and suggested their ranks should grow, as his administration presses ahead with efforts to boost imported supplies to help ease a nationwide shortage.

"We need more new entrants in the infant formula market," Biden said during a virtual meeting with executives from ByHeart, Bubs Australia, Reckitt Benckiser Group , Perrigo Company and Nestle SA's Gerber.

Multiple global suppliers are seeking U.S. approval to ship critical baby formula as Biden's administration accelerates what it has dubbed "Operation Fly Formula" to help fill store shelves and calm frustrated parents.

The approximately $4 billion annual sales U.S. baby formula market has historically been dominated by domestic producers, with imports limited and subject to high tariffs.

But U.S. parents have struggled to find baby formula in recent months after a February recall of some formulas by one of the nation's main manufacturers, Abbott Laboratories, coupled with pandemic-related supply chain issues.

The latest administration effort to solve the problem includes an announcement on Wednesday that United Airlines has agreed to transport U.K.-made Kendamil formula free of charge from Heathrow Airport in London to multiple airports across the United States over a three-week period.

This first shipment, which includes Kendamil Classic and Kendamil Organic formula, will be available at Target stores across the country in the coming weeks.

The administration also secured two flights totaling 380,000 pounds of baby formula from Bubs Australia that will be delivered to California and Pennsylvania on June 9 and June 11, respectively.

Biden said on Wednesday he only learned of the severity of the U.S. baby formula shortage in early April. The White House said it had been working around the clock since February to address the problem.

U.S. lawmakers have criticized the Food and Drug Administration (FDA) for not acting promptly to address the problems that caused the recall at Abbott's Michigan plant, which is set to reopen June 4.

The Biden administration has relaxed its import policy and invoked the Defense Production Act to help increase available U.S. supplies, which is still expected to take weeks. It has also said it could use federal resources to help transport supplies to retailers.

Two million cans of formula have been sent from the U.K., and Australian manufacturers are also preparing to send in more product.

Thorben Nilewski of Organic Family GmbH, which makes the popular Holle infant formulas, said in an email that the German company applied for the FDA’s temporary approval but has not yet received any feedback.

Many U.S. parents rely on baby formula. Fewer than half the babies born in the United States were exclusively breast-fed through their first three months, according to the Centers for Disease Control and Prevention's 2020 Breastfeeding Report Card.

The agency has said the company, which has the largest U.S. market share for infant formula, did not have a contingency plan to produce its specialty formulas that serve as the only source of nutrition for thousands of babies with metabolic disorders.

(Reporting by Jarrett Renshaw and Trevor Hunnicutt; Additional writing by Susan Heavey; Editing by Leslie Adler, Chizu Nomiyama and Aurora Ellis)