The Saville report into the killing of 14 civilians on Bloody Sunday will be published at the end of March, days after the Northern Ireland secretary, Shaun Woodward, reads the findings.
Woodward said he hoped to make Lord Saville's investigation public within days of receiving it.
But some of the families of those shot dead by British soldiers in Derry's Bogside on 30 January 1972 expressed concern that government lawyers would have the chance to scrutinise the report before they saw it.
At a meeting in Derry last night the relatives asked Woodward to give them the report at the same time as he received it. The report is to go to the government in the week beginning 22 March.
The families had previously criticised Woodward after being told they would not get the report until two weeks after the government. They said they feared it could be amended or have parts withheld by government agencies.
On Wednesday Woodward told the Northern Ireland affairs committee at Westminster that the report had taken too long to complete. He warned that it could languish in a warehouse for weeks if a general election was called.
Woodward promised he would only take about two weeks to consider the large document but said nobody knew when Gordon Brown would call the election.
The £200m inquiry was set up in 1998 to re-examine the Bogside shootings.
Meanwhile the Alliance Party leader, David Ford, met Bloody Sunday families last night and apologised for labelling the inquiry "pointless". Ford, who is tipped to be the new Northern Ireland justice minister, admitted his remarks were "clumsy and insensitive".