A graph is called \(K_{1,r}\)-free if it does not contain \(K_{1,r}\) as an induced subgraph. In this paper we generalize a theorem of Markus for Hamiltonicity of \(2\)-connected \(K_{1,r}\)-free (\(r \geq 5\)) graphs and present a sufficient condition for \(1\)-tough \(K_{1,r}\)-free (\(r \geq 4\)) graphs to be Hamiltonian.