North Yorkshire County Council said work by utility companies, which was set to conclude by the end of January, is "taking slightly longer than anticipated".
The third phase of the works that would have closed Stepney Road from January 31 has now been delayed. Scalby Road will now remain shut until mid-February; it was scheduled to close until January 28.
Northern Gas Networks is carrying out essential work to replace ageing metal pipework with new, more durable plastic pipes. The new pipes will ensure a safe and reliable gas supply and future-proof the infrastructure for alternative green fuels, such as hydrogen.
Richard Marr, county council Highways Area Manager, said: "We are working in conjunction with Northern Power Grid and Northern Gas Network to minimise future utility works in the area of the Crown Tavern junction.
"The utility works are taking slightly longer than was anticipated, however, our contractors are mitigating this by completing other works such as kerbing on Falsgrave Road. The closure on Stepney Road won’t be implemented until works have finished on Scalby Road."
The Northern Gas Networks said a lane closure will be in place on Falsgrave Road from January 31.
Scott Kitchingman, Business Operations Lead for Northern Gas Networks, said: "We would like to apologise in advance for any inconvenience caused during these essential works.
"However, it is vital we complete them in order to continue to maintain a safe and reliable gas supply to the residents of Scarborough. "
The county council said temporary two-way traffic lights are in operation on Falsgrave Road and that work to install new kerbs on Scalby Road to Falsgrave Road, new footpaths and a planting area adjacent to Cambridge Place is progressing. The authority said all trees which have been cut down will be replaced.
The major roadworks at the Scalby Road roundabout junction with Falsgrave and Stepney Road, outside the Crown Tavern pub, was set to cause disruption for three months, but with delays this could now be 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 is scheduled for completion on March 31.