Sulzberger said the reasons for her dismissal involved her management of the paper's newsroom.
But some have raised questions of sexism following reports that Abramson -- appointed in 2011 as the paper's first female executive editor -- was paid less than her male predecessor.
Sulzberger denied that was the case. He said Abramson's total compensation was "was comparable with (predecessor) Bill Keller's; in fact, by her last full year as executive editor, it was more than 10% higher than his."
While Abramson has stayed quiet, her daughter has been more outspoken in online postings. On Friday, she wrote, "The story isn't over, not even close."
--CNN Senior Media Correspondent Brian Stelter contributed to this report.