The backing comes as the shopworkers union Usdaw also backed the under fire Scottish Labour leader who has faced calls to quit after Labour lost 40 of its 41 Scottish seats last week.
Ms Harman’s comments came as the UK Labour national executive committee has announced an extended timetable to replace Ed Miliband as UK leader with a result announced at the party conference in September and shadow health secretary Andy Burnham has confirmed he is a candidate along with Liz Kendall and Chuka Umunna.
But focusing on the leadership controversy in Scotland, Ms Harman said: “Jim Murphy and Kez Dugdale have said that they will lead the rebuilding and renewal of the Scottish party. That is right and was backed by their Shadow Cabinet and group of MSPs on Monday.
“It’s for Jim and Kez to lead on policy, organisation and campaigning working with members, activists and affiliates.”
After initially declining an opportunity to back Mr Murphy, Ms Harman later issued a statement giving him her full support.
Earlier today, a spokesman had said: “Problems in Scotland are deep rooted and decisions about how to go forward should be a matter for the Scottish party.”
But there was further bad news for Mr Murphy as John Brown, regional secretary of CWU Scotland, said the union was likely to follow others such as Unite in calling for Mr Mr Murphy to resign.
Mr Brown said that the CWU had yet to agree a formal position, but stated that it was likely to call for the resignation of Mr Murphy, who lost his East Renfrewshire seat in last week’s election.
He said: “On a personal basis I think he should go.
“We’re having a conference call of our representatives to decide on a position, but on the soundings from our representatives the view seems to be that Jim should do the right thing and step down.
“I strongly suspect that the CWU position will be in line with that of Unison and Unite.”
Meanwhile, former first minister Henry McLeish said Scottish Labour said he was “neutral” on the issue of whether Mr Murphy should quit, but said the party had “learnt nothing” from its defeats in Scotland and had to embrace urgent reform.
But there was better news for Mr Murphy with Usdaw urging Scottish Labour to support him.
Lawrence Wason, Usdaw Scottish Officer, said: “There is no doubt that the general election result for Labour in Scotland could barely have been worse, but this is no time to turn on the leadership of the party. We need to keep our heads, quickly understand why the people of Scotland have, for the moment, moved away from Labour and focus on turning around the party’s fortunes at the Scottish Parliamentary Election next year
“Jim Murphy needs the time and our support to get the job done and a leadership contest now, which would be the second in a year, is not the answer. We must not engage in about of navel gazing, we must reach out to Scottish voters and shape a new direction for Labour.”
Mr Murphy has also been criticised by Unison while the GMB has called for a period of stability.