RNC Chairman Reince Priebus said he accepted the apology and called off a party-wide boycott of the left-leaning news and opinion network.
The Wednesday night message, sent from MSNBC's official Twitter account, said "the right wing" might object to a General Mills Inc. Cheerios TV spot featuring a biracial family.
"The tweet last night was outrageous and unacceptable," network President Phil Griffin said in a statement read on the air Thursday.
"We immediately acknowledged that it was offensive and wrong, apologized and deleted it," the statement said. "We have dismissed the person responsible for the tweet."
"I personally apologize to Mr. Priebus and to everyone offended," Griffin said. "At MSNBC, we believe in passionate, strong debate about the issues and we invite voices from all sides to participate. That will never change."
Priebus sent a letter to Griffin earlier in the day saying he banned all RNC staff members and surrogates from appearing on the network, which markets itself as "progressive," until Griffin personally and publicly apologized.
Priebus said he "asked Republican surrogates and officials to follow our lead."
After Griffin's apology, the RNC -- responsible for developing and promoting the Republican political platform and coordinating fundraising and election strategies -- said in a statement Priebus accepted Griffin's apology and called off the boycott.
"We will aggressively monitor the network to see whether their pattern of unacceptable behavior actually changes," the statement said. "We don't expect their liberal bias to change, but we will call them out when political commentary devolves into personal and belittling attacks."
The Twitter message that prompted the flap said, "Maybe the right wing will hate it, but everyone else will go awww: the adorable new #Cheerios ad w/ biracial family."
The Twitter message sought to tout an MSNBC story about the commercial, which will be broadcast during Super Bowl XLVIII Sunday.
Four weeks ago MSNBC host Melissa Harris-Perry made a tearful on-air apology for a Dec. 28 "photos of the year" segment in which she and a panel of comedians joked about a family picture featuring 2012 GOP presidential nominee Mitt Romney's family, including his adopted black grandson.
Romney responded saying he accepted the apology.
"I recognize that people make mistakes," he told "Fox News Sunday" Jan. 5. "And the folks at MSNBC made a big mistake. And they've apologized for it. And that's all you can ask for."