Editors’s Note: Obagi on April 3 announced that its initial suitor, Valeant, had raised its bid for the company to $24 a share, or more than $418 million, exceeding Merz’ offer on April 2.

Merz Pharma Group on Tuesday announced a $383 million bid to acquire physician-dispensed skin care products maker Obagi Medical Products Inc. of Long Beach, topping a previous offer.

The Frankfurt, Germany dermatology drug maker’s $22-a-share bid is 11 percent higher than the $19.75 offer that Obagi’s board accepted last month from Valeant Pharmaceuticals International Inc. of Montreal.

Obagi, which makes products that can be used after cosmetic surgery or to treat acne, aging and sun damage, said that the Merz bid was unsolicited but that its directors would consider it. The board “realizes that time is of the essence in this matter,” the company said in a statement.

Both companies are interested in Obagi’s 6,500-physician network, which they could use to expand their own presence in the United States. Analyst Annabel Samimy of Stifel Nicolaus & Co. noted that Merz may be more interested than Valeant in making the research and development investment to refresh Obagi’s older lines.

Samimy said in a note to investors that Valeant in the past has walked away from potential deals rather than engage in a bidding war. But Cantor Fitzgerald analyst Irina Rivkind believes Valeant at a minimum may consider matching Merz’s offer.

If not, “Obagi faces a $16.2 million termination fee if it walks away from Valeant, but we think that Merz would assume those costs as part of the transaction,” Rivkind said in an investor note.

Obagi shares on Monday closed up $3.17, or 16 percent, to $22.88 on the Nasdaq.