Mark Durkan MP asked the prime minister to "break the secrecy" on 700-odd files after six were released to the BBC.
The Home Office said it had no plans to bring forward a review of the files. The current release date is 2020.
The documents relate to an inquiry into the miscarriages of justice after the bombings, when the Guildford Four and Maguire Seven were wrongly jailed.
After Gerry Conlon's sister Ann demanded the immediate release of the remaining files, Mr Durkan wrote to Theresa May: "I write to you to urge that requests to release the rest of these documents be given every consideration."
He said: "Given your own decisive stand for transparency on other high-profile historic cases, I would urge you to break the secrecy seal on these files."
But a reply from Policing Minister Brandon Lewis at the Home Office said the files had a review date of 2019 agreed by the National Archives, subject to exemptions under the Freedom of Information (FOI) Act.
He said: "This department does not have any plan to bring forward the wholesale review of the files."
The SDLP draws most of its support from the nationalist community.
Since the first six files from Sir John May's probe into the convictions were released under FOI, further calls have been made for the rest to be opened.
Anne Cadwallader, from the Pat Finucane Centre human rights group, said papers were normally embargoed for 30 years.
On the 2020 release date, she said: "Four years is a long time. It's too late for Gerry, but his family members are still very concerned as are probably other family members of the other three."
Barrister Michael Mansfield QC called for continuing political pressure and said: "There needs to be constant questions in the House."
Prof Marie Breen-Smyth, an academic in Northern Ireland, said: "If any papers relating to the case are to be released, then all must be released."
The government has refused a request by the SDLP to consider releasing closed papers on the Guildford pub bombings.