Mr Singh's rebuttal came weeks after PM Modi alleged that although he met the then prime minister several times on the issue of raising the height of the dam, there was no assurance from the erstwhile UPA government on finishing the project.
"Modiji never held any meeting with me about the issue of the dam," Mr Singh said while replying to a question about the Narmada project at a press conference.
Refuting PM Modi's allegation that the project was stalled because the UPA government was "anti-Gujarat and anti-development", Mr Singh claimed that the previous Congress governments always supported the project.
During his Vadodara visit last month, PM Modi claimed that every time he went to meet Mr Singh to make a representation about the dam, the then prime minister used to express ignorance about the stalled work on it.
Gujarat Chief Minister Vijay Rupani hit back at Singh, insisting numerous representations were made in the past.