U.S. says nuclear arms talks with Russia productive

* U.S-Russia nuclear arms cuts talks "productive"

* U.S. calls for talks to ban fissile material

(Adds comments on disarmament talks, new quotes, byline)

By Stephanie Nebehay

GENEVA, June 4 (Reuters) - The United States said on Thursday that talks with Russia aimed at cutting stockpiles of nuclear weapons had made progress, before a July summit between the two countries' presidents.

Rose Gottemoeller, who led the U.S. delegation in the three-day Geneva round which ended on Wednesday, told the U.N.-sponsored Conference on Disarmament that she had held "productive talks with our Russian counterparts, working towards this START follow-on agreement".

Moscow and Washington are negotiating an accord to replace the 1991 Strategic Arms Reduction Treaty (START 1) which expires at the end of this year.

"We had very productive talks and we expect that productive trajectory to continue," she told Reuters after addressing the conference.

She urged the 65-member state forum to launch negotiations on a treaty banning production of nuclear bomb-making fissile material (plutonium and highly enriched uranium), widely seen as the next step in multilateral nuclear disarmament.

"This treaty has been on the international agenda for most of the nuclear age," said Gottemoeller, who is acting U.S. under-secretary of state for arms control and international security.

"It must be complemented by deeper respect for non-proliferation rules, consequences for those who violate them, improved verification of compliance and further progress on arms control," she added. (Editing by Jonathan Lynn)