The governor recently met opponents of the project, led by Siam Society president Bilaibhan Sampatisiri.
Ms Bilaibhan gave the governor a list of residents concerned about the environmental impact of the 5-billion-baht project, which encompasses a 9km flyover on top of Asok Montri Road.
Feasibility study reports prepared by consultants concluded the Bangkok Metropolitan Administration (BMA) should press on with the project, regardless of residents' concerns.
Ms Bilaibhan said the flyover is unlikely to ease traffic problems on the bustling road, but will aggravate environmental problems by preventing engine fumes from dispersing.
She also complained the consultants had falsely implied the project already had BMA approval.
"The BMA should clear the air on this matter," she said.
MR Sukhumbhand insisted the BMA has not approved the project because it requires further deliberation.
Nor has the BMA allocated money for construction, he said.
He insisted work will not begin during his term, which will end in the next three years.
But the governor refused to meet the demands of opponents by scrapping the project, saying more road space will be required to handle a higher number of cars.Bangkok deputy governor Jumpol Sampaongerng said work is a long way off, even assuming the project is approved by the BMA.
Land appropriation, a time-consuming legal process, will be required.
Mr Jumpol has proposed an alternative way for the BMA to solve traffic problems in the Asok area.
He said the city could expand road surfaces from 19 to 29 metres instead.
The deputy governor said the BMA has demarcated the expanded road surfaces in its traffic management plan.