The authority said work by utility companies has caused the delay, as earlier this month the works were running two weeks behind schedule.
Stepney Road, which was originally scheduled to shut from January 31, has now closed and Scalby Road is now fully reopened in both directions between the Crown Tavern roundabout and Manor Road roundabout., more than a month after the initial announcement that it would shut.
Temporary traffic lights will be installed at the Seamer Road-Falsgrave Road junction over this weekend, March 19 and 20. They will be in use from Monday March 21, as well as lane closures. This will allow the utility works to continue from the Crown Tavern junction to Seamer Road.
Resurfacing of these three roads will be completed under night-time closures from March 28 to 30, weather permitting. Stepney Road is now closed to vehicles but access to properties and businesses has been maintained.
Access to the Crown Tavern pub and its car park is maintained for drivers from the West side of the closure, as you approach from Stepney Hill, as well as pedestrians.
Nigel Smith, Head of Highways Operations, said: "We have worked closely with utility companies to incorporate their works into our schedule to reduce the disruption for road users and residents.
"Unfortunately the utility companies have faced delays so the scheme is approximately four weeks behind schedule."
The major roadworks were set to cause disruption for three months, but with delays, this has now been extended.
It is the last of four junctions around town to benefit from improvements in a £4m scheme; the upgrade is designed to ease congestion and improve safety, and initially was set to last for 13 weeks.
The junction will be widened and the existing mini-roundabout replaced with traffic signals. Scalby Road and Stepney Road will have new signal-controlled pedestrian crossings.
Work on the junction was originally scheduled for completion on March 31, but this has now been delayed to the end of April, the county council said.
Mr Smith added: "We would encourage people to avoid these junctions where possible and follow the signed diversions.
"If you do need to use the route please leave extra time for your journeys. We apologise for the inconvenience this will cause but ask the public for their patience during these final stages."
The diversion route from the south and west is either via the A165 Filey Road or the A64 Seamer Road/Queen Margaret’s Road/A165 Filey Road. The diversion route from the north is via the A165 Burniston Road.