Patrick Mercer MP has told Daybreak that the conclusions from the al-Sweady inquiry will "not be satisfactory."
He said the families "need to know the truth", but explained that both sides of the argument were "completely polarised".
Today an inquiry into the deaths of 20 or more Iraqis will begin, expected to last until 2014.
It is alleged that UK soldiers killed unarmed civilians and tortured detainees.
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Syrian government forces are continuing a push for total control of Aleppo, while a reported 20,000 civilians left the city on Saturday.
Rex Tillerson is president of Exxon Mobil and has close business links to Russian President Vladimir Putin.
Largely dry tomorrow with some sunshine in the south