The deadlock between the ministry and PSA had initially been broken after a day of Employment Court-ordered negotiations late last month.
Barclay said a vote will take place before the end of the working year.
"Our members took extended strike action as a last resort," Barclay continued.
"Our members have acted responsibly throughout and have been widely supported from within the courts and other workplaces they do so much to keep running, as well as from their fellow PSA members across the union and from other unions. I can't commend them enough for their resilience and solidarity."
The offer includes an across-the-board pay increase for July 2018 to June 2020, which equates to four per cent across two years, and a commitment to a Gender Pay Gap Action Plan Working Group.
An injection of more money to remedy historically low pay rates is also part of the deal, the PSA said, while a lump sum payment will cover back pay and wages lost from the strike action.
There is also a movement away from the ministry's performance pay matrix, supported by more funding to support transition to an agreed step-based pay scale and annual pay progression.
The ministry's chief executive Andrew Bridgman said in a statement to the Herald he was unable to comment on the details of settlement while the PSA holds ratification meetings.
During the industrial action security concerns were raised by New Zealand Law Society president Kathryn Beck and New Zealand Bar Association (NZBA) vice-president Jonathan Eaton QC after a brawl in a Christchurch courtroom.
The Employment Court was also called on to determine an injunction application by the ministry to stop the short-notice "lightning strikes" because of safety concerns.
The court dismissed the application, but Bridgman maintained his position that the lightning strikes were "unsafe and irresponsible".
The PSA's industrial action included work bans, work-to-rule activities and a refusal to serve, check and sign legal documents - leading to a logjam of adjourned cases at the country's busiest courts.