No. They measure two entirely different properties – mass and volume. These are related through a separate property – density.
The mass of a kilogram is partly defined by volume – 1000cm^3 of water at room temperature and pressure has a mass of 1kg, provided it has no impurities, this volume is equal to 1 liter.
So one liter of water has a mass of one kilogram. If something has a different density than pure water, or the temperature/pressure vary then the mass contained within one liter will no longer equal one kilogram.
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