The Federal Government has offered to make sweeping amendments to another key anti-espionage bill as it presses Parliament to pass its full suite of laws cracking down on foreign interference.

Yesterday, a bipartisan parliamentary committee hammered out a compromise on a bill introducing tough new penalties for foreign interference and sabotage, paving the way for it to pass Parliament this month.

But it still has not got Labor's backing for another contentious piece of legislation which would force those lobbying on behalf of foreign governments to put themselves on a public register.

Charities, universities and some business groups have all criticised the bill, and the Catholic Church has even warned it could force the faithful to register as agents of the Vatican.

The Government has insisted both bills are needed to combat the "rapidly escalating" threat of foreign interference and is making fresh overtures to Labor to secure its support.

Last night, Attorney-General Christian Porter said he would dramatically narrow the scope of the register so "only organisations or individuals ultimately working at the direction of a foreign government or political party" would have to put their names on the list.

"Under these amendments, the vast majority of private international companies would not be considered foreign principals unless it can be shown they are closely related to a foreign government or political organisation," Mr Porter said.

Universities have warned some researchers who accepted funding from foreign governments — or who worked with colleagues overseas — could be unfairly entangled in the scheme.

But Mr Porter said the Coalition would tighten the language in the bill to make it clear no-one would have to register merely because they took money from — or collaborated with — overseas organisations.

Labor has been deeply scathing of the foreign agents register, calling the bill's drafting "sloppy" and "hopeless".

But the Attorney-General will be hoping the amendments will be enough to win over the Labor MPs on the Joint Committee on Security and Intelligence who were crucial to yesterday's compromise.

Mr Porter insisted it was critical for the Government's new framework to be in place before the "Super Saturday" of five by-elections on July 28, and "be fully operational before the next scheduled general election".

"It's vital that our national security legislation and framework reflects the modern challenges that we face, and this bill and that framework remains dangerously incomplete while these two remaining and critical bills remain unlegislated," he said.

Repercussions 'downright terrifying'

Meanwhile, civil society groups are railing against the bipartisan deal struck yesterday to increase penalties for espionage and to make it illegal for foreign agents to interfere in Australia's political system.

Claire O'Rourke from Amnesty International Australia said both major parties were "trampling over" freedom of expression.

"Under this bill charities, including Amnesty, who hold the Australian Government to account on its human rights record could face criminal charges — this is not only outrageous, it's downright terrifying," she said.

"This is clear government overreach and a cynical exercise by both sides of politics to shield themselves from the scrutiny of Australian civil society, including charities."

And Morry Bales from the Law Council said he remained concerned about the potential for the changes to limit freedom of expression.

"Parliament is the one that needs to convince the Australian people that these, in some cases, very draconian laws are actually needed," he said.

"We'll be looking at parliamentarians and we ought all to be holding them to account to make sure this is a responsible piece of legislation."