Thirukkural-On Virtue-Truthfulness-Kural-298

Rajaji's translation is most effective.

Water makes for external cleanliness; Truthfulness is the detergent of the heart.

Water is the agent for outer cleanliness; inner cleanliness comes with truth.

There is also the implication that 'inner cleanliness comes first' (i.e.) that truthfulness is more important. Apparswamigal expressed the same idea when he said,

"Vaaimaiyae thooimaiyaaga
Poosanai eesanaarku"