MOSCOW—Russian President Vladimir Putin urged the West on Thursday to move quickly to meet Russia’s demand for security guarantees precluding NATO’s expansion to Ukraine and the deployment of the military alliance’s weapons there. Speaking during a marathon annual news conference, the Russian leader welcomed talks with the U.S. that are set to start in Geneva next month, but warned the discussion focused on Moscow’s demand needs to produce quick results. “We want to ensure our security,” Putin said. “We put it straight: there must be no further expansion of NATO eastward.” Last week, Moscow submitted draft security documents demanding that NATO deny membership to Ukraine and other former Soviet countries and roll back the alliance’s military deployments in Central and Eastern Europe. A key principle of the NATO alliance is that membership is open to any qualifying country. The United States and its allies have said they won’t give Russia …