Several proposals are being considered by the Home Office
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Human rights campaigners have urged caution over plans to make it a crime to "associate" with terror suspects.
The proposal being considered by the Home Office could see people jailed if they ignore warnings not to contact certain groups or individuals.
A similar law was introduced in France several years ago after bombings by terror groups originally from Algeria.
An Amnesty International spokeswoman told BBC News Online it was almost impossible to define "association".
Very successful
"Is it a chance meeting or is does it mean having strong ties with terrorist groups?" she said.
She said it could mean people were jailed for being friends with someone suspected of terrorism.
A Home Office spokesman said it was a question of striking a balance between ways of dealing with the threat of terrorism and respect for human rights.
He told BBC News Online: "We think it's right to look at how other mature liberal democracies have tackled the problem.
"This has been very successful in France."
The government wants to stop those on the fringes of extremist groups being drawn into acts of terror and to make it more difficult for terrorists to get help and support from members of the public.
Detained indefinitely
They would issue a formal warning to all known contacts of suspects or radical groups.
The French "associating with a wrongdoer" law allows people to be arrested and prosecuted for being linked with a group planning a criminal act.
The arrested person can be detained indefinitely.
Amnesty has repeatedly opposed such detentions as "an aberration of justice, the rule of law and human rights".
Proper judicial oversight of any proposed new measure was absolutely imperative, the Amnesty spokeswoman added.
The law change is part of a series of measures under consideration by the Home Office to tackle the terrorism threat to the UK.
Amnesty would be making representations and putting forward suggestions to the Home Office about the plans, the organisation's spokeswoman confirmed.