Labour and Liberal Democrat whips have met to discuss suspending pairing arrangements for absent MPs when the House of Commons returns in September, the Guardian understands.

The two parties held talks in recent days about a possible suspension, but no agreement has been reached.

Last week the Conservatives’ chief whip, Julian Smith, prompted a bitter row when he told his paired MPs to breach Commons voting conventions in knife-edge Brexit votes.

The majority of MPs refused the request, which has been acknowledged by party sources, and only the Conservative chair, Brandon Lewis, went through the voting lobbies.

Lewis was paired with the Lib Dem MP Jo Swinson, who was on maternity leave. He later apologised to her for the breach, as did Smith, and both said it should not have occurred.

Pairing is a convention that allows MPs to cancel out each other’s votes when they must be away from the Commons. Tory sources have conceded it was an error to ask Lewis to break his pair.

Labour sources said the party had not ruled out suspending the arrangements when parliament returns in September. A number of close votes are coming up in the autumn, including the final vote on any Brexit deal and on the withdrawal and implementation legislation.

In the key vote last Tuesday when Smith asked MPs to break their pairs, the government won by six votes. Other votes that week were won with majorities of as small as three.

A Labour source said the party was not ruling out any option from September. Another said it would not be fair to spring the change before a key vote and that the party would want to be clear in advance that it would not pair its MPs.

Another senior Labour figure cast doubt on the effectiveness of such action, pointing out the party has three MPs either pregnant or currently on maternity leave – Laura Pidcock, Cat Smith and Holly Lynch – as well as a number of others with serious medical conditions or ongoing personal circumstances.

The Lib Dem chief whip, Alistair Carmichael, confirmed his party was actively considering suspending pairing, though he said he was torn because it was the only way for the party to provide satisfactory maternity cover for Swinson.

“There will have to be some step taken by the Tories, beyond what they have said already, for the system to work again,” Carmichael said. “I have had an apology but I also need an explanation. I cannot countenance ruling out suspending pairing until I get a better one than the government has offered so far.”

No decision is expected to be taken until after the summer recess. A suspension of pairing would be difficult for both the government and opposition but would be likely to cause more trouble for the government, which regularly pairs ministers when they are away on official business.

Labour and the Lib Dems would not be the first parties to withdraw from pairing arrangements. The SNP has a long-term policy that it does not make such deals.

Theresa May’s Commons majority narrowed even further on Tuesday as MPs voted to suspend the DUP MP Ian Paisley for 30 days after he failed to declare two family holidays paid for by the Sri Lankan government. He will be absent for some of the key Brexit votes.

The DUP has a confidence-and-supply arrangement with the government for its 10 MPs to support the Conservatives on important legislation.

MPs voted in favour of a motion to suspend Paisley proposed by the Commons leader, Andrea Leadsom, after a ruling from the parliamentary commissioner for standards.

May’s deputy, David Lidington, has promised the government will call a debate on proposals for proxy voting for new parents in September, which could lead to absent MPs being allowed to designate a colleague to vote on their behalf rather than abstain with a pair.