The £50 billion project has attracted a string of compensation claims from residents living near the proposed route.
A Government committee said applications from terminally ill people must be considered urgently.
In their report, published before the election, the HS2 committee stated: "Another issue was the lack of an adequate expedited process in cases of terminal illness.
"The new scheme must rectify this. We expect urgent applications to be considered urgently."
However, the Department for Transport said that such applicants would instead get a phone call within two days, and be updated on the progress of their application, going on to say: "We feel that in such circumstances, this approach would be a far more appropriate and productive method of dealing with a case as opposed to setting more stringent deadlines for the processing the case which could simply result in a poorer quality decision from the independent panel."
To try to speed compensation claims along, the committee demanded: "There should be a mechanism whereby those in areas of particular blight can avoid the need repeatedly to approach local estate agents for evidence of inability to sell." However, the Department for Transport rejected this proposal citing: "Difficulties in defining the limits of what constitutes a 'neighbouring' property."
The committee report also asked how extensively the new compensation schemes have been advertised.
Stop HS2 campaign manager Joe Rukin said: "The committee of MPs scrutinising HS2 have asked them to be humane, and do the right thing in fast-tracking compensation claims for those who are terminally ill. The committee said they wanted a system whereby people in an area blighted by HS2 wouldn't have to jump through so many hoops to get compensation.
"In telling people about the new compensation scheme, they seem to think a social media campaign consists of a few retweets, and while they thought it was necessary to tell everyone within a kilometre about the compensation consultation, they trimmed that to 300 metres when it came to telling people about the final scheme itself."