The offer was sent to the Education Institute (NZEI) on Friday afternoon, before bargaining scheduled for Tuesday.
NZEI union members are expected to vote this weekend on whether to accept the new offer or move to a vote on strike action.
The offer is an increase of between 2.7-4.6 percent during the next two years.
Sir Brian said there was no room to move further on remuneration.
The Ministry of Education previously offered teachers three one percent pay rises over three years, before NZEI members held two weeks of stop-work meetings in August for primary schools and principals, including support staff and Ministry of Education learning staff.
NZEI said teachers felt undervalued and pay offers needed to ensure teachers didn't go backwards, given the rising cost of living. Earlier this year, it said smaller classes and more teacher aides were needed to ensure all children had quality learning.
