GENEVA (Reuters) - The United States expects to make further progress with Russia in talks aimed at cutting nuclear weapons stockpiles before a July summit between their two presidents, a top U.S. arms control official said on Thursday. We had very productive talks and we expect that productive trajectory to continue, Rose Gottemoeller, who led the U.S. delegation in the three-day Geneva round, told Reuters after addressing the United Nations-backed Conference on Disarmament. Moscow and Washington are negotiating an accord to replace the 1991 Strategic Arms Reduction Treaty (START 1) which expires on December 5. The two sides are seeking to narrow differences before U.S. President Barack Obama and Russian President Dmitry Medvedev meet in Moscow on July 6-8. Our Presidents have directed that we report by July on our progress in working out a new agreement, Gottemoeller, who is acting U.S. under-secretary of state for arms control and international security, said in a speech to the Geneva forum. Kremlin spokeswoman Natalya Timakova told reporters in Moscow this week that it was not excluded that at least an outline deal could be wrapped up in time for the summit. Obama and Medvedev have said the new arms deal should cut stockpiles below those in the 2002 Strategic Offensive Reductions Treaty (SORT), under which both sides are to cut their arsenals to between 1,700 and 2,200 warheads by 2012. Russia has said it wants to link the nuclear talks to U.S. plans to deploy an anti-missile shield in Europe and has pushed for the United States to put a limit on the number of delivery systems the rockets or other means that deliver weapons. The round ended on Wednesday without either side commenting. Gottemoeller also said that time was ripe for negotiations on a treaty banning production of atomic bomb-making fissile material (plutonium and highly enriched uranium), widely seen as the next step in multilateral nuclear disarmament. The 65-member forum, breaking a deadlock of more than a decade, last week agreed on a work plan that would include negotiations on a so-called fissile cut-off treaty (FMCT). There should be no misapprehensions or illusions on the difficulty of our task, Gottemoeller warned the conference. This treaty has been on the international agenda for most of the nuclear age. It is time that we stopped talking about having an FMCT and got to work to complete it, she added. Clinching a fissile pact would be a step towards nuclear disarmament, but the finish line is a vision conveyed by Obama a world free of nuclear weapons, Gottemoeller said. Without naming names, she called for deeper respect for international rules aimed at preventing the spread of nuclear weapons as well as consequences for those who violate them. The forums members include the five official nuclear powers Britain, China, France, Russia and the United States India and Pakistan, both nuclear-capable, Israel, widely believed to have the Middle Easts only nuclear arms, and North Korea.