In a statement, Sunny Jain, Unilever's president of beauty and personal care, acknowledged the product suggested "a singular ideal of beauty”.
However, some have criticised Unilever for declining to remove the products entirely.
“I cannot see how this does anything apart from damage the brand and make it look greedy, when it has been pointed out repeatedly, how this product makes them fuel and profit colourism and oppression,” British writer Poorna Bell said on Twitter.
Two separate petitions urging Unilever to cull the Fair & Lovely range have been signed by more than 18,000 people in the last few weeks.
It follows a move by US multinational Johnson & Johnson to stop selling its Clean & Clear Fairness line of products in Asia and the Middle East.
“Conversations over the past few weeks highlighted that some product names or claims on our dark spot reducer products represent fairness or white as better than your own unique skin tone,” Johnson & Johnson said in a statement.
“This was never our intention – healthy skin is beautiful skin.”
About 6,277 tonnes of skin lightener were sold worldwide last year, according to Euromonitor International, including products marketed as anti-ageing creams targeting dark spots or freckles.
Band-Aid, which is owned by Johnson & Johnson, earlier this month launched a range of bandages in “light, medium and deep shades of Brown and Black skin tones that embrace the beauty of diverse skin".
Colgate has also announced changes to a popular Chinese toothpaste brand called "Darlie", which was called "Darkie" until 1989. It is still marketed as "black person toothpaste".
US companies have faced particular pressure to revisit the branding of their products, some of which have drawn complaints of racism for years.
PepsiCo last week said it would end the Aunt Jemima line of pancake syrup and batter adorned with the face of a black woman, while Mars plans to "evolve" the Uncle Ben's brand of rice dishes that uses a black man as its logo.
The Aunt Jemima brand has existed for more than 130 years, and "has evolved over time with the goal of representing loving moms from diverse backgrounds who want the best for their families," according to PepsiCo.
In February, agribusiness Land O'Lakes released new packaging for its dairy products, removing a female Native American mascot that had attracted criticism, though the company didn't mention race in announcing the change.
In Australia, comedian Josh Thomas this month called for Coon cheese to be renamed, given the word is used as a racial slur against Indigenous Australians.
On its website, Saputo Dairy Australia says the cheese is named after its US creator, Edward William Coon, who “patented a unique ripening process that was used to manufacture the original cheese”.
Additional reporting by Reuters, AFP.