Lawyers for the group said on Thursday that they would hold off from filing the suit this month as planned and give the British government until January to decide on an apology and agree to negotiate an out-of-court settlement.
Martyn Day, the plaintiffs' British lawyer, said: "Next week, we'll write a letter to the British government, they will have three months to respond on whether they want to sit down with us and seek a solution to the claims.
"If they don't respond, then we will take the case to court in January. We call on the British government to act and at last pay compensation to these people so that they receive the justice they deserve."
The veterans announced in May that they would file a lawsuit in London on October 20, the 54th anniversary of the arrest of famed Kenyan independence leader and founding president Jomo Kenyatta.
They are seeking unspecified reparations for Mau Mau veterans who claim they were tortured by colonial authorities in the 1950s.
But Day and other lawyers representing them and the Kenya Human Rights Commission said they wanted to give the British government a chance to respond to the allegations, apologize and pay compensation.
Paul Muite, a Kenyan lawyer, said: "It's not just compensation we are seeking. We want Britain to acknowledge before Kenyan eyes and the international community that they violated human rights and restore the human dignity of people who suffered."
The Mau Mau, which started as a grassroots movement among the Kikuyu tribe to recover arable farmlands appropriated by British colonial settlers, evolved into a fully-fledged rebellion in 1952 that demanded Kenyan independence.
Its hit-and-run tactics against white settlers prompted a heavy-handed response from colonial police and allied home guards who rounded up thousands of young Kikuyu men and allegedly brutalised and tortured many.
Surviving Mau Mau fighters, now in their 70s and 80s, claim they and their colleagues were made to suffer cruelty such as summary executions, torture, rape, beatings, forced labour and evictions.