The report acknowledged parties' past diversity efforts, including all-women shortlists by Labour and the Conservatives' "A-list" of approved candidates.
The Conservatives and Liberal Democrats are also being urged to make sure more women get elected despite their rejecting calls for all-women shortlists.
Labour is under pressure to introduce all-women shortlists, especially in areas like Wales, Scotland and the North East of England where there are fewer women MPs.
Cardiff North MP Julie Morgan, who is in favour of all-women shortlists, said their adoption was needed to end a situation in which just seven female MPs have ever represented Welsh seats.