"The Prime Minister directed me to meet water resources minister Pawan Bansal," Chandy said.
Chandy's meeting with Singh came a day after the Prime Minister told Tamil Nadu chief minister Jayalalithaa that nothing should be said or done to create "undue alarm". Tamil Nadu has accused Kerala of whipping up a 'fear psychosis' on the issue.
The chief minister had also met Congress chief Sonia Gandhi earlier in the day to brief her about Kerala's position on the issue.
Chandy, in his first communication to Jayalalithaa after the latest row erupted, wrote a letter to her seeking a reduction in the water level in the reservoir to 120 feet as an immediate step to remove the fears of lakhs of people living close to the dam.
Singh had on Thursday directed Bansal to arrange an early meeting between officials of Tamil Nadu and Kerala to "sort out outstanding issues and allay genuine concerns".
Kerala says fears about the weakness of the 116-year-old dam had increased after the area around the site was shaken by 26 tremors in the last five months alone.
While Kerala apprehends that rising water level in the dam poses a major risk to it, Tamil Nadu rejects any such fears.