In the job since 2011, Hiesinger, 58, presided over the conglomerate`s protracted exit from its volatile steel business, whose roots go back more than 200 years and formed the company`s backbone for many generations.
Having joined Thyssenkrupp from engineering conglomerate Siemens
Activist shareholders Cevian and Elliott, the latter of whom disclosed a stake in the company in May, have both criticised Thyssenkrupp`s performance under Hiesinger, with shares down 28 percent since he took office in January 2011.
Hiesinger said in a statement: "I take this step very consciously to enable a fundamental discussion in the supervisory board on the future of Thyssenkrupp."
"A joint understanding of board and supervisory board on the strategic direction of a company is a key pre-requisite for successfully leading a company."
Thyssenkrupp`s supervisory board will meet on Friday to take a decision on the request from Hiesinger.
Cevian, which holds a seat on Thyssenkrupp`s supervisory board, has repeatedly called for a more fundamental restructuring of the sprawling group, which makes everything from elevators and chemical plants to ships and car parts.
This, the European fund previously said, could result in Thyssenkrupp looking for strategic solutions for all of its business units and turning itself into a holding company that is invested in several sectors.
"Thyssenkrupp`s conglomerate strategy and matrix organisation have failed," Cevian founding partner Lars Foerberg said on Sunday.
Cevian declined immediate comment on Thursday, as did hedge fund Elliott. They jointly hold about a fifth of the company.MORE AGGRESSIVE OVERHAUL
Shareholder criticism also mounted following a joint venture deal with Tata Steel agreed over the weekend, with some criticising that terms had not been favourable enough and that Hiesinger could have sought a better deal.
Frankfurt-listed shares in Thyssenkrupp
"We expect Hiesinger`s departure to be interpreted positively as a sign Thyssenkrupp may consider more aggressive restructuring measures including the potential spin-out of `jewel-in-the-crown` assets such as Elevator Technology," said Jefferies analyst Seth Rosenfeld, who rates Thyssenkrupp "buy".
Analysts have said a public listing of the group`s elevator business, its most profitable, would make sense, as would a joint venture with one of its rivals, which include Finland`s Kone
Other options include a sale of Thyssenkrupp`s Materials Services, its raw-materials distribution arm that is the group`s biggest division by sales.
Breakups of conglomerates meet more resistance in cultures such as Germany`s than in the United States, however, as labour leaders and other stakeholders have more influence.
Supervisory Board Chairman Ulrich Lehner said Hiesinger had freed the company from an existential crisis during his tenure.
"Without Heinrich Hiesinger there would be no Thyssenkrupp today," he said in a statement. "I am deeply grateful for what he achieved."
Meantime, labour representatives voiced concerns over the now more-likely scenario of a break-up of Thyssenkrupp.
"I fear that the remaining company will be broken up locust-style," said Wilhelm Segerath, head of Thyssenkrupp`s works council who also sits on the group`s supervisory board, referring to the term used by some in Germany for activist investors.
"This must not happen."
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