The PSNI is disclosing information to the Omagh Bombing Inquiry "as quickly as it can", its legal team has said.
The pledge came after the overall pace of disclosure was deemed to be not fast enough by counsel for the proceedings.
Paul Greaney told inquiry chairman Alan Turnbull that the legal team had hoped that information from relevant bodies would have been more advanced than it is.
He said the inquiry would use its powers to ensure the fullest possible levels of disclosure.
The inquiry also heard from counsel for former RUC chief constable Ronnie Flanagan that he is sorry for the impact that a public spat he had with the then police ombudsman over a critical report had on the bomb victims.
Meanwhile, one of the lawyers who represent some of the survivors and bereaved families urged the Irish Government to live up to its promises in relation to assisting the proceedings.
The Real IRA bomb in the Co Tyrone town in August 1998 killed 29 people, including a woman who was pregnant with twins - the worst single atrocity in the Troubles.
The public inquiry is examining whether the explosion could have been prevented by the UK authorities.
Counsel for the Police Service of Northern Ireland Philip Henry said the force had implemented a new team for the Omagh Bombing Inquiry review, adding that the organisation offers its sincere condolences to those who lost loved ones and its deepest sympathy to all those affected.
However, he said there were significant challenges and limitations associated with old, outdated and non-interconnected information technology systems as well as paper records.
As an example, Mr Henry said, an electronic system that stores criminal investigation papers on the atrocity holds 26,000 documents of varying length and 2,000 exhibits.
In addition, he said the "magnitude of the request" by the inquiry to provide material in connection with 31 previous and attempted attacks from 25 years ago is "a huge undertaking".
"It is important to emphasise that the PSNI is not offering this as an excuse. Rather, it is a candid explanation of what is involved, so that expectations are realistic as to how quickly it is possible to reliably meet the inquiry's requirements.
"The PSNI recognises that any periods of delay can cause frustration. However, the PSNI must also do the work properly, and it is being done as quickly as it can, and in good faith."
Mr Henry outlined how it took more than three months for three highly trained sensitive researchers to investigate the first three of the 31 previous incidents identified by the inquiry.
It was believed that it would have delayed proceedings by several years if the PSNI did not allocate additional resources to the process.
While the force is also dealing with more than 1,100 other pieces of legacy-related litigation, it decided to reassign all of its sensitive researchers who were working on other cases to join the work on the 31 previous incidents for a period of six months.
Mr Henry said this "exceptional step" was done in the knowledge that it may impact on work on other legacy-related cases.
"However, if it did not adopt this course then there would be a delay of several years in progressing the inquiry, which was unacceptable to the PSNI, unacceptable to the inquiry, and would have been unacceptable to the other core participants."
Mr Henry said it will not be possible for the force to disclose all information in an open, public format, but said the service would apply for restriction orders only to protect the public interest or national security and to comply with the European Convention on Human Rights.
On the subject of making concessions, he said the PSNI will do so if it becomes appropriate.
However, it was not possible at this point in time, counsel said, as it is still in the process of reviewing thousands of documents.
Mr Henry also said the PSNI believed that the examination of the preventability of the bombing needed to be calibrated with reference to what was reasonably practicable in the circumstances.
He added that a fair and balanced examination would also have to look at other demands and threats faced by the police at the time.
Finally, he noted that it is "much easier to join the dots after the event, when one already knows the outcome" as he said the inquiry must be aware of "hindsight bias".
Read more: Omagh inquiry: The victims remembered
In his opening statement, counsel Stephen Toal, acting for some of the survivors and bereaved families, was critical of both the Irish Government for failing to set up its own inquiry into the attack and also the UK government for requesting redactions.
"This inquiry did not begin with candour, it began with resistance," he said.
"Both governments now speak of support, they make warm statements about solidarity but these families have learned to measure words against deeds.
"To this day the Irish Government has not provided full cooperation, they refuse to establish a parallel inquiry.
"To these families their involvement often feels more like a performance than a sincere commitment.
"Then came the British government’s recent application for redactions which did little to build confidence among these victims. It speaks to a defensive instinct, not a transparent one.
"That is why we say talk is cheap, trust must be earned through conduct, not through words."
Mr Toal added: "These families do not want scapegoats, they do not seek to vilify police officers who responded on the day.
"Those officers are rightly regarded as heroes but they do demand answers from the institutions that were supposed to protect them.
"They expect this inquiry to identify what intelligence was held in the lead up to Omagh, examine why it was not acted upon, expose any systematic failures particularly across borders and recommend reforms to ensure it never happens again.
"Above all, they expect the truth."
Opening statements are to continue tomorrow.
