Four-year-old Sean Turner, from Wiltshire, died in March 2012 at Bristol's Royal Hospital for Children.
A coroner ruled the hospital had not failed Sean but his parents Steve and Yolanda disagreed and tweeted Prof Sir Bruce Keogh to "sort this out".
Within hours Dr Keogh responded that he would be in contact to "fix a date".
Sean suffered a brain haemorrhage and cardiac arrest six weeks after he had undergone corrective heart surgery at the Bristol hospital.
His parents blamed doctors and nursing staff for transferring their son from intensive care too soon and for missing the signs of his worsening condition.
But in a narrative verdict at the inquest last month, coroner Maria Voisin said there were "lost opportunities" in Sean's care, but it did not amount to neglect.
After Mr Turner, 47, tweeted Sir Bruce, saying: "Will someone please pick up the reins, stand to post and sort this out?".
Within 24 hours, NHS England's medical director had responded: "Steve, I will meet all concerned parents. Will contact you on Monday to fix a date convenient to families. This week?".
Mrs Turner said they had been "gobsmacked" when they got the response.
"We never expected Sir Bruce to tweet back," she said.
She added they initially thought it was a "hoax".
An NHS spokesman confirmed the tweet was genuine and said a meeting would be set up "at the earliest opportunity" for Sir Bruce "to hear them voice their concerns and to understand their concerns".
Although Mrs Turner said it would not be "practical to meet all concerned parents this week", she said they would be "waiting for his call".
The NHS's medical director has agreed to meet the parents of a boy who died after heart surgery after they pleaded with him on Twitter.