"Today, I met with the Russian delegation. Tomorrow, we'll meet with the Chinese delegation, among others," a senior State Department official told reporters in Geneva, asking not to be identified.

The United States had held "preparatory" meetings with Russia and with China in Washington after the New START treaty lapsed earlier this month and the meetings in Geneva were "a little bit more substantive", the official said.

Washington had also spoken with nuclear powers Britain and France "on multiple occasions" in recent weeks, the official added.

New START, the only remaining treaty between the United States and Russia that limited deployment of nuclear warheads, expired on February 5 as US President Donald Trump called for a new agreement that also includes Beijing.

China's nuclear arsenal remains far smaller than those of Russia and the United States but it has been growing quickly. China has publicly rejected calls to enter negotiations on a new three-way treaty.

Christopher Yeaw, the US assistant secretary of state for arms control and non-proliferation, told the Conference on Disarmament in Geneva that New START had been seriously flawed and "did not account for the unprecedented, deliberate, rapid and opaque nuclear weapons build-up by China".

Chinese ambassador Shen Jian pushed back, telling the conference that Beijing would not "engage in any nuclear arms race, with any country".

"China's nuclear arsenal is not in the same league as the countries possessing the largest nuclear arsenals," he said.

"It is not fair, reasonable or realistic to expect China to participate in the so-called trilateral talks."

The senior US official said Trump was encouraging "multilateral negotiations, multilateral strategic stability dialogue and arms control negotiations that will eventually lead to a better agreement".

The official said the "the next logical, natural step is to bring this to the P5" -- the five permanent members of the UN Security Council: the United States, Russia and China, plus Britain and France, who are also nuclear weapon states.

But that "is only one possibility", with bilateral, multilateral or plurilateral formats also possible, the official said.

"We're not going to constrain ourselves to a particular format of negotiations or dialogue," the official stressed.

"We're going to use every tool and format that we can, and that what that achieves some progress toward that goal of a better agreement (towards) fewer nuclear weapons."