MOSCOW (Reuters) - The United States and Russia have held two days of successful talks on ways to slash vast stockpiles of Cold War nuclear weapons, a Russian diplomat said on Wednesday. Finding a replacement for the 1991 Strategic Arms Reduction Treaty (START I) before it expires on Dec 5 could herald a thaw in relations between the worlds biggest two nuclear powers. Obama and Medvedev last month ordered officials to begin the complicated talks needed to find a replacement for START, one of the biggest arms reduction deals in history. The talks were held in a constructive spirit, we consider they were successful, a Russian diplomat told Reuters after the first round of formal negotiations ended on Wednesday. He gave no details on where progress had been made. The diplomat said the next round of talks would be held in Geneva on June 1-3 and that a progress report would be made to Obama and Medvedev at their meeting in Moscow on July 6-8. We agreed that the first results of work on a new agreement will be reported in the forthcoming meeting in early July in Moscow, the diplomat said. The talks are complicated by Washingtons plan to station elements of an anti-missile system in Poland and Czech Republic, in order to intercept rockets fired from what it sees as rogue states, such as Iran. Russia says the plan will undermine its national security. EQUAL SECURITY Foreign Minister Sergei Lavrov on Wednesday said the United States must allay Russian concerns over the missile system to achieve a breakthrough in the nuclear weapons talks. The fundamental principle of an agreement must be equal security for both sides and the preservation of strategic parity, he told reporters at the 19th century mansion where the talks took place. This of course cannot be ensured without taking into account the situation with anti-missile defence. Obama said last month that the United States would go ahead with the anti-missile system if Washington thought there was a continued threat from Iran. But a study published on Wednesday by the East-West Institute, a think tank, said the system would have great difficulty distinguishing between warheads fired from Iran and the decoys that might accompany them. The proposed shield cannot provide a dependable defence for Europe or the United States against Iranian missiles, it said. Lavrov said the nuclear talks should also take account of any plans for space-based missiles and the development of highly destructive non-nuclear weapons. Finding a deal could warm relations between Russia and the United States after bitter arguments under former US President George W. Bush over missile defence, NATO expansion and last Augusts war between Russia and Georgia. The negotiators face tight pressure to work through scores of complicated technical issues including differences over how to count nuclear weapons and ensure compliance before the December 5 deadline for replacing START.