Mr Hunt met with bosses at business groups including the Confederation for British Industry (CBI), Institute of Directors (IoD) and UKHospitality earlier on Wednesday afternoon.
The meeting came following calls from industry for urgent clarity after the Government delayed setting out details that were originally due before the new year.
Next week the Government will outline the conclusion of its review into its current support scheme in the House of Commons, the Treasury revealed in a statement.
The current energy bill relief scheme, which caps wholesale energy prices on electricity and gas at about half the expected market price, ends in March.
“The Government has protected businesses this winter from these high energy costs through the £18 billion Energy Bill Relief Scheme – one of the most generous support packages in Europe,” the Treasury said.
“However, no Government can permanently shield businesses from this energy price shock.
“The Chancellor was clear that this level of support is unsustainably expensive and that the current scheme was always time-limited to six months.”
It claimed that extending the scheme in its current form could “cost tens of billions of pounds” depending on wholesale energy prices.
The Chancellor heard concerns from business leaders over the current pressure caused by sky-high energy prices during the meeting.
The Treasury added that Mr Hunt told the chiefs that a “lower level” of further support would “be designed to help them transition to the new higher price environment and avoid a cliff edge in support”.
Households have already been told that their bills will be capped until April 2024, albeit at a higher rate than the current £2,500 annual cost, while firms have been kept in the dark.
The revised scheme is expected to offer help with bills for a further year, until March 2024.
Mr Hunt had promised to give firms certainty over future plans for support by the new year, saying last month the announcement would come just before or just after Christmas.
Mr Hunt said at his autumn budget in November that the Government would have to target support only at the most vulnerable industries and would likely also have to lower the aid they receive.
Business groups railed against the plans, warning over job losses and company failures if universal support is withdrawn.
While ongoing help for companies is set to be welcomed, there are concerns over a drastic cut to support.
On Wednesday, the IOD urged the Government for targeted support in its plan next week following the meeting.
Alex Hall-Chen, principal policy adviser for sustainability, skills and employment at the IOD, said: “The Energy Bill Relief Scheme has been a crucial intervention, with our research showing that it removed a serious risk to around a quarter of businesses this winter.
“Businesses will be reassured that support will continue in some form for a further 12 months.
“However, it is a shame that the government has not found a way to target the support to those sectors of the economy particularly exposed to volatile international energy markets.
“This means that the most vulnerable businesses will lose support at a critical time compared to what they have had this winter.”
The British Beer and Pub Association (BBPA), which was also in the meeting, said pubs could be forced to shut without help close to current levels.
“We met with the Chancellor today to underline the challenges the industry face and the critical importance of extending the energy relief support to avoid significant business failure and the closure of many pubs and brewers,” commented chief executive of the organisation, Emma McClarkin.
“Without extended support at close to current levels, pubs and brewers in communities across the country could be lost for good.
“The failure to safeguard pubs and breweries from price increases come April will be the last straw for businesses who have been struggling for three years to remain solvent and serving their communities.”