Ministers are rethinking changes to copyright law before a vote in parliament next week, in a further concession to artists, the Guardian has learned.

A source close to Peter Kyle, the technology secretary, said proposals to introduce an opt-out system of copyright rules was no longer his preferred option but one of several being given consideration.

The proposed changes, which would allow AI companies to train their models using copyrighted work without permission unless the owner opts out, have been criticised by creators and publishers. High-profile artists including Paul McCartney and Tom Stoppard have backed a campaign against the changes.

Kyle said: “We’re listening to the consultation and we are absolutely determined to get this right. We’re not going back to square one. We are moving forward.”

“We can’t pretend we can outlaw training in other countries who have their own copyright law, but we can build a system which works in the United Kingdom. Some elements of the consultation haven’t even featured in the debate so far.”

“We will be working hard to come up with practicable solutions to the very complex issue of how we enable both the creative industries and UK AI companies to flourish. We will report to parliament on issues of transparency and licensing and try to find some common ground on which we can agree.”

Ministers have consulted on changing copyright law with the opt-out system as their “preferred option”, but government sources said Kyle was now looking more broadly at different proposals.

The government is particularly interested in encouraging licensing agreements between AI companies and creators as a way of ensuring creators are paid for their content.

But campaigners are concerned ministers could fall back on a free-for-all system instead of requiring AI companies to follow existing copyright law. Government officials said the law needed to change to attract AI investment to the UK and give creators control over how their content was used in the future.

Beeban Kidron, the cross-bench peer and prominent campaigner, said: “I am glad to hear that the government no longer sees an opt-out proposal as the preferred option but … for this change to be in any way meaningful it must include an unequivocal commitment from the government to protect copyright holders right now.”

Next week MPs will vote on the data bill, which has been used by critics including Lady Kidron as a vehicle to derail the proposed opt-out system. On Thursday, Kyle tabled amendments to the legislation intended to mollify critics by committing to an economic impact assessment of different potential changes, including the opt-out system and a licensing system.

Ministers are braced for a political row over opposition amendments to the data bill. Both the Liberal Democrats and Conservatives are considering a ban on under-16s from social media, a cause which has previously attracted support from Labour MPs.

The Tories are also drawing up an amendment seeking to record people’s birth at sex as part of digital verification processes, sources said. A Labour source described it as a “naked attempt to reopen a running sore” over sex and gender after the supreme court ruled last month that the term “woman” was defined by biological sex.

The data bill faces further hurdles when it returns to the upper chamber. Kidron will move to reinstate her copyright amendments and Tim Clement-Jones, the Lib Dem tech spokesperson in the Lords, said it was possible the bill could be struck down entirely. He said concessions on transparency, or requiring AI firms to reveal what copyright-protected content has been used to create their products, would have to be made.

The government’s offer to carry out an economic impact assessment of copyright changes within 12 months of the data bill passing has also led to concerns that this could push the process to the end of Labour’s term in 2029.

“The world is moving exceptionally fast, and the government is moving very slow,” said Owen Meredith, the chief executive of the News Media Association, whose members include the Guardian. “Delay means change to the underlying copyright framework could not materialise until the very tail-end of this parliament.”

Kidron said a four-year delay to clarifying the AI copyright regime was a “completely inadequate timescale”. “The creative industries will be dead on their feet by then.”