In the past, companies would "quite happily" give up a permit as more would come on stream with subsequent block offers, she said.
"That isn't going to happen because we won't be doing further offshore block offers," Woods said.
Instead, she is hitting "the pause button" on the clause while the oil and gas sector works out how it will manage the new exploration environment.
"This is just about working constructively with industry as we figure out the managed transition that we have over the next forty or so years."
The Greens disagree with Woods' call; its energy Spokesperson Gareth Hughes said it is offering mining companies special treatment.
"[Companies] shouldn't be offered special treatment to extend or waive that time limit."
He said he struggles to see the point in banning offshore exploration for oil and gas if existing companies with huge blocks can hold off from exploring until way later down the track.
The policy has been embraced all over the world, Hughes said – "let's not water it down. I am urging her to reconsider this proposal".
Woods said she understands the Green Party's concerns which they are "perfectly entitled to."
She said the Greens were made aware of the decision "as part of our Government arrangements."
"They said they weren't supportive."
Last night, the Ministry of Business, Innovation and Employment (MBIE) released its regulatory impact statement (RIS) on the exploration ban policy.
It revealed the estimated economic costs of the policy would be $8 billion, between 2027 and 2050.