A complete moratorium on such shipments was imposed after the accident and an urgent report was commissioned by Mike Heron QC.
After a Cabinet decision, Agriculture Minister Damien O'Connor said the rules would be relaxed - but only partially and not until after 23 October.
"Given the Heron advice, the director general of agriculture will be in a position (after that date) to make calls on whether animals can be moved offshore," he said.
"But it will be conditional, it will not be going back to where it was, and there may be changes in those conditions."
There are about 27,000 animals that were caught out by the moratorium and are now being kept in special containment areas at a cost of about $5 per head per day.
Livestock exporters said they were relieved to learn that some of them might now be able to be moved.
But further details of just how many will not be available until after the Heron inquiry has filed its verdict.
Debra Ashton from Save Animals from Exploitation (SAFE) accused the government of pre-emptive behaviour.
She said she was disappointed that Cabinet had approved conditional exports before the Heron review was finished.
Even worse, there was a second, separate review, on the whole question of live exports from A to Z - and that was not finished either.
"We were surprised to hear that Cabinet approved a conditional prohibition ahead of this review," she said.
"This signals to us that the Labour-led government is still very keen to continue live exports despite the risk to animals.
Ashton said the government should have waited until all the facts were in before making policy.
- RNZ
