Obagi Medical Products Inc. on Wednesday said that its initial suitor had increased its bid to more than $418 million, exceeding a rival bid announced yesterday.

Obagi, a Long Beach company which makes physician-dispensed skin care products that can be used after cosmetic surgery or to address signs of acne, aging and sun damage, said that Valeant Pharmaceuticals International Inc. of Montreal has offered to pay $24 a share.

The Obagi board approved the deal, it said, and recommended that stockholders tender their shares in favor of Valeant’s offer, which will expire on April 23. Valeant’s initial $19.75-a-share offer, announced last month, totaled less than $344 million.

Merz Pharma Group, a Frankfurt, Germany, dermatological drug maker, on Tuesday made what Obagi had described as an unsolicited offer to buy Obagi for $22 a share, or more than $383 million. In a statement, Merz said it had been in “ongoing” talks with Obagi prior to announcement of the first Valeant offer, and was unaware that Obagi was planning to sign a deal with another company so quickly.

Wednesday’s developments sent Obagi shares up $2.29, or 10 percent, to $25.16, in Nasdaq midday trading.

Obagi reported $120 million in sales last year. Merz, which makes prescription and over-the-counter treatments for neurological and metabolic disorders as well as dermatology, said Obagi would be a “natural fit” that would diversify its dermatology portfolio and expand its presence in the U.S.

“Merz has the necessary cash on hand to fund the transaction and does not require additional due diligence,” Mertz said Tuesday. It has not yet commented on today’s counter-offer from Valeant.

Obagi, which faced $16.2 million termination fee if it backed out of the initial deal with Valeant, agreed to raise the fee to $21 million in exchange for higher offer.