Labour’s legislation, agreed as part of a framework with the Irish Government, will put in place a reformed Legacy Commission with enhanced powers.
The Conservative Party and others are concerned it will lead to more investigations of military veterans.
The bill aims to repeal the existing Legacy Act, which included a conditional immunity clause, later found unlawful by the Northern Ireland courts.
Davis claimed the Northern Ireland Troubles Bill, which had its second reading in Parliament on Tuesday, is affecting morale in the SAS, and its ability to recruit and retain soldiers.
He said: “The Prime Minister knows that last week nine four-star generals made plain the bill is doing harm to the British Army already.
“Most acute damage is being felt by the Special Air Service.
“As a result, lawyers for the SAS Regimental Association have sent a letter before action to the Secretary of State for Northern Ireland.
“I know of no precedent for this in the entire history of the British Army, and … it reflects how important it is.”
He went on: “Can I make a plea to the prime minister?
“Will he involve himself personally to make sure that 60, 70, 80-year-old soldiers, who have carried out actions which most of us would view as heroic, are not persecuted in the coming years, because now it’s a matter not of national security, but of national honour.”