The Counter-Terrorism and Security Bill would allow the home secretary to impose temporary exclusion orders on British terror suspects.
There have been calls for ministers to change the proposals to allow judicial oversight of the orders.
In other measures, universities and councils would be required to take steps to counter radicalisation.
The new legislation, which receives its second reading in the House of Lords on Tuesday, also includes:
Under the exclusion orders proposal, Home Secretary Theresa May would be able to sign an order to ban a suspected extremist from returning to the UK, for up to two years at a time.
The individual could return if they agreed to some kind of investigation or monitoring arrangements to ensure they were not a threat.
Labour has called for a judge to have a role when the orders are imposed.
This view was echoed by David Anderson QC, the government's independent reviewer of terror legislation.
He told BBC Radio 4's The World at One: "If you are going to give these very powerful instruments to the home secretary to decide that she believes someone is a terrorist and they should be constrained in their movements for two years or so, you have absolutely got to have proper judicial safeguards, otherwise you end up fuelling the whole grievance agenda that is at the root of the terrorism in the first place."
Immigration and Security Minister James Brokenshire said the measures contained in the bill were a "considered and targeted" response to the terror threat,
"These important new powers will only be used when it is necessary and proportionate and are subject to stringent safeguards and oversight," he added.
Peers are to debate the government's counter-terrorism bill, which will give new powers to the security services.