Road chiefs are hoping to install a temporary bridge on Grinton Moor after the previous structure was destroyed by flooding.
North Yorkshire County Council says it hopes to restore the route later this month.
However, repairs to the Reeth to Richmond road is due to take much longer.
Dave Bowe, corporate director of Business and Environmental Services at North Yorkshire County Council, said they were working hard to reopen the small number of roads which remain closed as quickly as possible.
He added: “Our commitment is clear in the speed with which we removed tonnes of mud and rocks from many rural routes and in our determination to resolve the more complex issue of the key B6270 which links the upper dale to Richmond.
“In addition to the clearance operations we have been carrying out detailed assessments of the roads and bridges including inspections by specialist geotechnical engineers so we can produce a detailed plan for reinstating the road network as quickly and safely as possible.
“In terms of the B6270, there are two problems to overcome here; the rush and force of the flash floods have caused a landslip which has damaged a section of carriageway near Cogden Heugh to the east of Grinton which has removed over a quarter of the highway width in that location and further towards Grinton there is significant damage to the bridge over Cogden Beck which means that the bridge needs to be replaced.
“Together these present a significant challenge but one we are working hard to overcome.
“Public safety will be our priority and clearly we are still in the early stages of understanding the scale of the problem, but we are aiming to carry out temporary bridge and carriageway repairs which would allow access under traffic management to this route by mid-August and then two-way traffic flow before the end of September.
“These are our target dates and while we obviously hope to meet them; we are in the hands of the elements and as such we will provide regular updates as the project progresses.
“We recognise that the current diversion route means longer journeys and we want a solution that’s safe and practical as soon as possible.
“In addition to our works on the B6270 we will also be working hard to reopen the C106 road that runs from Grinton towards Leyburn which has been temporarily closed following the collapse of Grinton Moor Bridge.
“We are also planning to install a temporary structure in this location with a target date of the end of August. In addition to the temporary solutions required to safely reopen these roads we will set about the work required to deliver permanent replacement bridges as soon as possible.
“We want to send a clear message out to everyone that we are doing everything possible to support them in practical ways.
“Alongside our focus on the roads we are also coordinating our army of volunteers who signed up for our Ready for Anything team. They are out today helping us understand the personal impact on householders, so we can work with partners to solve as many problems as possible.
“We are also looking to get our mobile household waste recycling unit out into communities so that residents who need to, can get rid of damaged property once they have spoken to their insurance companies.”