Speaking after a visit to Dromara in County Down, one of the worst affected areas, Mr Robinson said: "Staff currently on the ground are doing vital work, but we also need to consider all other avenues to ensure that we reach those cut-off as soon as possible.
"It has been for that reason I spoke to the Secretary of State this morning and asked her to consider providing assistance, including from the Territorial Army."
His plea came as hundreds of people remained cut off and without power following the freak snowstorm that has left parts of Northern Ireland at a standstill for more than four days.
DUP Assembly member Paul Frew urged Stormont Executive ministers to back the call for help from the TA.
Mr Frew asked Regional Development (DRD) Minister Danny Kennedy, who has responsibility for the roads, and Department of Agriculture and Rural Affairs (Dard) Minister Michelle O'Neill to contact the military.
"The Territorial Army are in place for emergencies such as this and the engineering teams will have heavy plant which could help clear routes," he said.
"Whilst DRD staff have been working hard, it would be sensible to supplement their efforts with the TA personnel to speed the process along. Many farmers are facing significant loss of livestock because of the conditions.
"The TA will also have the ability to erect temporary shelters if they are needed.
"Whilst Dard will not have machinery at its disposal, the Minister should recognise the emergency situation which exists and the dire need for help within some communities."
Snow drifts and abandoned vehicles continue to hamper efforts to restore power to 800 homes and businesses cut off when blizzard conditions hit.
The TrafficwatchNI website said roads remain closed due to snow accumulations, with worst affected areas including Ballymoney, Antrim and Larne in the northern division, and the south Down area around the Mournes and Dromara Hills.
Newtownabbey, Lisburn and parts of North Down were also affected.
Two helicopters are assisting in the operation to get engineers to the affected properties, all of which are located in rural and exposed areas.
More than 140,000 customers who lost power when the wintry blast struck the eastern counties of the region last Thursday and Friday have since had supply restored.
Many farmers have been particularly badly hit by the severe weather, suffering livestock fatalities and damaged properties. Snow drifts in some areas are as high as 18 feet.
In a statement on Monday night, Chief Superintendent Chris Noble said: "We are all working hard to get the supplies to those in areas where vehicular access is difficult.
"Some of these people have now been snowed in for four days and it is vital we ensure they have adequate food and medical supplies.
"While there has been an improvement in conditions in many areas, there are still hazardous conditions in a number of areas."
For updates on road closures and weather follow us on Twitter at @BelTel
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