Chris Heaton-Harris has been urged to publish details of concessions offered to the DUP as part of the near year-long effort to get Stormont restored.
The secretary of state said before Christmas that negotiations with the DUP over its concerns around the post-Brexit trade arrangements had concluded.
The DUP rejected last February’s EU-UK Windsor Framework deal and have since been seeking assurances over Northern Ireland’s place within the UK single market.
On Wednesday, the assembly will be recalled in the latest bid to get the institutions restored, beginning with a proposal to elect a speaker, ahead of nominating a first and deputy first minister.
The latest recall, the sixth since the DUP’s Paul Givan resigned as first minister almost two years ago, is sponsored by Sinn Féin and comes against the background of escalating industrial action by public sector workers over a pay dispute.
Previous recalls have not been successful because the DUP has vetoed the election of a speaker.
Ahead of the recall, Sinn Féin first minister designate Michelle O’Neill said her party’s focus was on restoring the executive and “urgently delivering a fair pay deal for public sector workers”.
“It is decision time for the DUP – there can be no more delays or excuses,” she said.
“Our public sector workers play a pivotal role right across our society, working in our hospitals, schools, on trains and buses, and within the civil service – they are entitled to a pay rise and they should get it now.”
As MLAs gather at Stormont in what is widely expected to be another vain attempt to elect a speaker, there have been calls for Mr Heaton-Harris to make public the fruits of months of British government engagement with the DUP.
Alliance deputy leader Stephen Farry said the DUP had been “indulged for almost a full year in closed negotiations”.
“However, other parties and stakeholders have an interest in the outcome,” he said.
“With the negotiations at end and the deadline for the assembly about to pass, there is a strong case for openness and transparency on what is on offer.”
SDLP Stormont leader Matthew O’Toole described the British government’s negotiations as “clandestine”
“Public sector workers whose pay deal is being withheld, those on health service waiting lists and families struggling due to the cost of living have a right to know what deal is on the table, while the DUP continue to drag their heels and put internal party squabbles above the interests of people here,” he said.
Ulster Unionist leader Doug Beattie, who first called for British government concessions to be made public last month said: “If unelected DUP party officers know what is in the deal, there is no reason why it should not be shared with all executive parties.”
A spokesperson for the secretary of state said his focus was on restoring the executive.