The grocer dismissed reports it had planned to change the names of international food items like "Trader Jose" and " Trader Ming's"
Trader Joe's said it disagrees with accusations of racism and said it does not make decisions based on petitions.
In a statement last week, Trader Joe's said "We make decisions based on what customers purchase, as well as the feedback we receive from our customers and crew members. If we feel there is need for change, we do not hesitate to take action."
The grocer also said the names of its international foods "show appreciation for other cultures."
The petition calling for the renaming of the products said, "The Trader Joe's branding is racist because it exoticizes other cultures - it presents 'Joe' as the default 'normal' and the other characters falling outside of it - they are 'Arabian Joe,' 'Trader José,' and 'Trader Joe San.'"
The petition has garnered more than 5,000 signatures.
Earlier this month, the company said it decided several years ago to use only the Trader Joe's name on its products and has been in the process of updating the ethnic-sounding labels.
"While this approach to product naming may have been rooted in a lighthearted attempt at inclusiveness, we recognize that it may now have the opposite effect - one that is contrary to the welcoming, rewarding customer experience we strive to create every day," company spokeswoman Kenya Friend-Daniel said at the time.
Friend-Daniel went on to say that packaging for a number of the products had already been changed, and the company expected to complete the process "very soon."
The Associated Press contributed to this report