In a statement issued on Tuesday, Sparkes said: "Recent events have generated deliberate misinformation and a misunderstanding about the RNLI – our purpose, our tasking, and particularly our lifesaving work in the Channel.
"Sadly, as a result, some of our volunteers and staff have been the subject of online and, in the worst cases, physical abuse.
"The RNLI's people represent the very best in our society, they selflessly give up their time to keep others safe."
He continued: "We will take whatever steps we can, to care for and protect our people and their families."
Digital Secretary Lisa Nandy said she had spoken with tech firms about how the names, addresses and photographs of RNLI staff and volunteers were reportedly shared online.
She was responding to Vikki Slade, the Liberal Democrat MP for Mid Dorset and North Poole, about "some very disturbing posts" on social media identifying "brave RNLI rescuers".
Nandy was asked what more the government could do to remove posts "that put children and adults' safety at risk through doxxing".
She told the Commons: "It is something that the government is concerned about [and] I'm personally concerned about."
Requests to accept the landing of RNLI boats carrying the migrants were refused by both Portsmouth harbour and Southampton Port, the BBC understands.