Chris Heaton-Harris said he was aware that the energy market in the region was significantly different to the one in Great Britain.
On Wednesday, the Government is expected to outline further details on how state-funded mitigations against spiralling energy bills will be applied in Northern Ireland.
Earlier this month, Prime Minister Liz Truss tabled plans for an “energy price guarantee”, with a pledge to cap average household bills at £2,500 for the next two years.
At the time, the Government acknowledged that a different approach would be required in Northern Ireland but did not outline any details, other than a pledge that a “similar” level of support will be offered to people in the region.
Northern Ireland’s market has its own regulator and does not have the energy price cap system that operates in the rest of the UK.
A higher percentage of householders in the region rely on home heating oil than fellow consumers in GB.
The picture is potentially complicated further by the absence of a functioning devolved executive in Northern Ireland.
The DUP has blocked the formation of an executive in protest at Brexit’s Northern Ireland Protocol. Some ministers remain in post in shadow format but they are limited in the decisions they can take.
On a visit to Belfast on Tuesday, Mr Heaton Harris said: “I know there is a specific market identity in Northern Ireland.
“On my first day, I’d only been in the job less than 12 hours, we had questions to me on the floor of the House and lots of people made the point that 68% of people here in Northern Ireland use heating oil for their primary source of heat.
“So, we have a specific market and a specific problem and I’ve been working across government to try and find a good solution that works.”
Mr Heaton-Harris highlighted that some support payments have already be paid to eligible recipients in Northern Ireland.
On Tuesday, £150 was set to be paid out to some welfare claimants and pensioners.
DUP Economy Minister Gordon Lyons said Northern Ireland should be included in a UK-wide scheme.
“Some of those details are still being worked out, we clearly have a different way in which our energy system works here in Northern Ireland,” he told the PA news agency.
“But I’ve always believed that the best way and the quickest way to get money to people was directly through a UK-wide scheme and I believe that’s what will happen.”
Mr Lyons said he did not expect all the details to be confirmed this week.
“Well, I think that there’ll always be a little bit of teasing issues out and that applies to the whole of the of the UK, there will be a number of issues that need to be addressed,” he said.
“And we will see the broad picture of where it is that we are at. But I’ve made clear in my conversations with UK Government ministers that this support is essential, and it needs to happen as quickly as possible, and I believe that we will see progress on that.”
The Government has also committed to delivering a £400 energy bill discount to people in Northern Ireland.
There had been uncertainty how the scheme, which was announced earlier this year, would be rolled out in the region without a functioning ministerial executive.
Last month, the Government said it would be delivered “as soon as possible” but did not set out a firm timeframe.
At the time, Mr Lyons said he believed the scheme would be delivered in November by way of a one-off lump sum to energy companies.
On Tuesday, Mr Lyons expressed confidence that timetable could still be met.
“I hope that that will still be the case,” he said.
“Obviously, the death of her majesty the Queen has meant that Parliament hasn’t met over the last 10 days. Legislation will need to be brought forward for that scheme.
“But I still believe that we’re on track to get that up before the end of this year. But I hope sooner, and I still think that it’s possible that will happen.”