Coexistence of ferromagnetic fluctuations and superconductivity in the actinide superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>UTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

We report low-temperature muon spin relaxation/rotation (<i>μ</i>SR) measurements on single crystals of the actinide superconductor UTe₂. Below 5 K we observe a continuous slowing down of magnetic fluctuations that persists through the superconducting transition temperature (<i>T</i> _<i>c</i> = 1.6 K), but we find no evidence of long-range or local magnetic order down to 0.025 K. The temperature dependence of the dynamic relaxation rate down to 0.4 K agrees with the self-consistent renormalization theory of spin fluctuations for a three-dimensional weak itinerant ferromagnetic metal. Our <i>μ</i>SR measurements also indicate that the superconductivity coexists with the magnetic fluctuations.