Catalyzes the formation of UDP-N-acetylmuramate (UDP-MurNAc), a crucial precursor of the bacterial peptidoglycan cell wall, from UTP and MurNAc-alpha-1P. Is likely involved in peptidoglycan recycling as part of a cell wall recycling pathway that bypasses de novo biosynthesis of the peptidoglycan precursor UDP-MurNAc (PubMed:23831760). Is able to complement the fosfomycin sensitivity phenotype of a P.putida mutant lacking murU (PubMed:23831760). H(+) + N-acetyl-alpha-D-muramate 1-phosphate + UDP = phosphate + UDP-N-acetyl-alpha-D-muramate Cell wall biogenesis; peptidoglycan recycling. Monomer. Belongs to the nucleotidyltransferase MurU family.