Asked about the US-UK extradition treaty which has been described as "one-sided", Attorney General Dominic Grieve QC said there were "underlying fundamental problems that are not very easy to address".
"I think there's a lack of public confidence in the US justice system," he said.
There were perceptions in Britain that the US justice and penal systems were "harsh and disproportionate", leaving Britons "uneasy and uncertain", he added.
He told the MPs these concerns were "not readily curable".
More top news
You can't say the 130 Brexit Tory MPs who forced Cameron to have this referendum haven't had an impact on political life, writes Chris Ship.
Foreign Secretary Philip Hammond said there will have to be a "trade-off" on UK access to the EU single market and migration controls.
A man arrested on suspicion of murdering Melanie Hall 20 years ago has been released on police bail. She disappeared in Bath in 1996.