The row came as LibDem Business Secretary Vince Cable told MPs the UK Government's industrial strategy – which he will unveil in a speech today – would include targeted state support for key sectors such as advanced manufacturing, higher education, the digital industry and the energy supply chain.
While the strategy of "picking winners" had failed in the 1970s, Mr Cable said there had been "a swing of the pendulum too far in the opposite direction" in subsequent decades.
He added the UK could learn from countries like Germany and Finland, where governments work in partnership with key industries.
Chuka Umunna, his Labour Shadow, welcomed the move but asked whether Mr Cable had "unequivocal backing" from David Cameron, George Osborne or even his own team at the Department for Business.
Mr Cable insisted he had the "absolutely full support" of the Prime Minister, Chancellor and business colleagues.
Meantime, Mr Fallon confirmed the department would announce measures later this week to deregulate employment rules to encourage negotiated settlements of disputes instead of tribunals.
Mr Cable insisted the measures would not allow bosses to "fire at will" but would "deal with the burdensome nature of hiring and firing".
Earlier, he unveiled a "radical" plan to curb red tape by tackling the regulations which have most impact on businesses.
Brendan Barber, the TUC's General Secretary, said that restricting health and safety inspections to firms in higher-risk areas would fuel an "occupational health epidemic".