Engineering manager Leslie Miley wrote that he was asked to build a tool that would classify recruitment candidates' ethnicity by analysing their last name.
The idea was intended to improve diversity among staff.
Alex Roetter, Senior Vice President of Engineering, said that the "engineering-driven, quantitative solution" was a "blind spot".
"As an engineer, I understand this suggestion and why it may seem logical," wrote ex-employee Mr Miley on blog-publishing platform Medium in which he also claimed to have been the only African-American member of Twitter's engineering leadership team.
"However, classifying ethnicities by name is problematic as evidenced by my name.
"What I also found disconcerting is this otherwise highly sophisticated thinker could posit that an issue this complex could be addressed by name analysis."
In 2014 only 4% of Twitter's technical staff were black or Hispanic, according to its own figures.
Mr Roetter said that Mr Miley's comments about him were "inaccurate" but that he was sorry for the "pain and confusion" caused by his communication.
"I realise that we have blind spots, myself included. One of mine is that I have a tendency to default to engineering-driven, quantitative solutions," he responded.
"We all want the same resultsâ€Š - â€Šstronger representation of under-represented minorities at all levels within Twitter."
Mr Miley said that he was passionate about Twitter as a high-profile platform for comment around issues like the Ferguson shootings and the success of the hashtag #BlackLivesMatter.
"And yet there were moments that caused me to question how and why a company whose product has been used as an agent of revolutionary social change did not reflect the diversity of thought, conversation and people in its ranks," he wrote.
Mr Miley cited occasions when a network for black engineering colleagues was not invited to internal events attended by high-profile black visitors such as Jesse Jackson and Ben Jealous, chief executive of the NAACP (National Association for the Advancement of Colored People).
"Is it because, as one colleague told me, 'they forgot that you were black?'," he said.
"When Hillary Clinton and Mellody Hobson [chairman, Dreamworks Animation] visited, the Twitter Women Engineering resource group was notified and given an opportunity to meet privately."
Mr Roetter said the firm is taking its commitment to increased diversity seriously.
It has published its own diversity goals for 2016, which includes increasing the proportion of "under-represented" minority staff to 11%, and aiming to ensure that 35% of its staff are women.
A senior Twitter executive has replied to criticism from a former employee about the firm's approach to diversity.