By Alissa de Carbonnel and Steve Gutterman

MOSCOW (Reuters) - Russia said Thursday the United States had to allay its concerns about conventional warheads and weapons in space if it wanted further cuts in the two countries' nuclear arsenals.

In an annual news conference, Foreign Minister Sergei Lavrov said warmer relations had brought a "noticeable improvement in the international situation" in the past year -- praise for U.S. President Barack Obama's "reset" of ties with Russia.

He pointed to the New START treaty, signed by Obama and Russian President Dmitry Medvedev in April, which will commit the Cold War foes to limits of 1,550 warheads on deployed strategic missiles and bombers.

But with Russia's parliament expected to ratify the pact this month, Lavrov signaled that deeper reductions -- including cuts in Moscow's large arsenal of shorter-range tactical nuclear weapons -- would be difficult to secure.

"We are convinced that before talking about any further steps for nuclear non-proliferation, the START treaty agreed with the United States must be fulfilled," Lavrov said.

Obama has set out a vision of a world without nuclear weapons, which Russia says it shares. Between them, the two nations have about 95 percent of world's nuclear weapons.

When the U.S. Senate approved the New START treaty last month, it ordered Obama to seek talks with Moscow within a year on reductions of tactical nuclear stockpiles.

But Lavrov said discussions of future nuclear arms cuts "must take into account other factors that increasingly influence strategic stability."

"Let's imagine that everyone abandons nuclear weapons, but that in parallel non-nuclear strategic weapons are developed ... that may be even more effective in military terms -- what then?"

His comments reflected Moscow's concern that the United States could develop or deploy weapons that would weaken Russia's nuclear might and upset the balance of power.

In addition to long-range missiles with conventional warheads, Lavrov expressed particular concern about the possibility of "the militarization of space."

In 2006, U.S. President George W. Bush signed an order opposing Washington's participation in treaties that would restrict its right to develop space-based weapons. In July, a U.S. arms control official said the United States could consider proposals to limit or ban weapons in space.

(Editing by Andrew Roche)