Work on a bypass in Carmarthenshire will not begin until 2025 at the earliest, a letter from Welsh Government says.
Construction had been planned to start on the £50m Llandeilo road by the start of 2019.
Plaid Cymru accused the Welsh Government of breaking a promise made in a budget deal with the party in 2016.
The Welsh Government said it remained committed to the scheme.
Residents in Llandeilo have been calling for action for four decades - the town suffers from congestion from lorries driving through the main street.
The route, which is on the A483, is currently used as a route from Swansea to join the A40 to the Midlands.
Transport Minister Ken Skates had promised "shovels in the ground" by the end of 2019.
Earlier this year it was confirmed work had been delayed until autumn 2022 at least.
But in a letter to the area's Member of the Senedd, Plaid Cymru leader Adam Price, Mr Skates laid out a new potential timetable for the project, with short, medium and long-term measures.
Constructing a "Llandeilo relief road" is listed as a long-term measure, pegged for at least five years away.
Short-term measures, to be implemented within a year, include new traffic lights, removal of parking and loading bays on Rhosmaen Street and additional public parking.
Medium-term measures would include "footway enhancements", improved bus connections from Llandeilo railway station and a "Ffairfach relief road" at Ysgol Bro Dinefwr.
Mr Price, MS for Carmarthen East and Dinefwr, said: "This is yet another broken promise and the Welsh Government has completely undermined the agreement it entered into with Plaid Cymru in 2016.
"To face a third delay on this project is completely unacceptable - particularly as air pollution levels are higher than the national standards, and the problem will be only be getting worse."
The bypass's inclusion in the budget for 2017-2018 had been criticised by Labour MS Lee Waters at the time, who warned about "pork barrel" budget deals.
Mr Waters, who is now a deputy transport minister working in Mr Skates' department, cautioned against offering schemes "for political parties to show they have exerted influence".
The letter added that a consultation event on the scheme had been delayed from earlier in the year, and is now being planned for September.
A Welsh Government spokesman said: "To ensure we deliver the maximum benefits we are carefully following detailed appraisal processes, as well as ensuring the feedback from stakeholders and local voices is taken into account. This is in the context of restrictions in place from coronavirus which are affecting the way we can work.
"We continue to work with stakeholders, including Carmarthenshire County Council, to make improvements in the short, medium and long-term. We remain committed to delivering the scheme as part of wider efforts to improve transport in the area."