The long-awaited replacement to the Strategic Arms Reduction Treaty (Start) - which expired on December 5 - is a pillar of the so-called reset in relations between the Cold War foes.
As Thursday's talks opened, Clinton said bilateral relations between Washington and Moscow had "moved in a very positive direction" since she met with Lavrov one year ago.
Barack Obama, the US president, and Dmitry Medvedev, his Russian counterpart, called for a quick signing at their Moscow summit in July, but negotiations stalled over issues of counting, verification and US plans for a missile defence system in Europe.
Neave Barker, Al Jazeera's correspondent in Moscow, said Russian concerns over the US missile defence plan could still throw treaty plans off course.
"Earlier on this afternoon the deputy foreign minister said the irresponsible deployment of missiles could affect whether the Start treaty goes ahead on schedule," he said.
The broad aim of the new treaty is to reduce the number of nuclear weapons to between 1,500 and 1,675, from the 2,200 currently allowed.
But despite thawing relations, Clinton urged Russia to delay the launch of Iran's first Russian-built nuclear reactor, which is expected to go online this summer.
Her comments came after Vladimir Putin, the Russian prime minister, made the announcement about the plant in the southern city of Bushehr on Thursday.
Russia has been helping Iran build the plant since the mid-90s, but its launch has been marred by a series of delays.
The issue is controversial, coming as Western powers attempt to pressure Iran to curb its nuclear programme, which they believe is aimed at developing atomic weapons.
Clinton said it would be "premature" to go forward with launching a nuclear power plant in Iran due to a lack of assurances from the Islamic state about its intentions.
"We are as committed as we have been to a diplomatic solution, but there must be a solution. Iran is not living up to its international obligations," she said.
Russia is constructing or gearing up to construct nuclear reactors in a host of countries, including China, India and Bulgaria.
Clinton arrived in Moscow on Thursday and was to be joined by George Mitchell, Obama's special envoy to the Middle East, for talks with diplomats from Russia, the EU and the UN.
They were to discuss the crisis in US-Israeli relations and stalled efforts to restart Middle East peace negotiations.
Clinton was meeting one-on-one with Lavrov, and the two were then to meet their UN and EU colleagues on Thursday night.
Together they form the so-called Quartet of Middle East peacemakers who are scheduled to hold formal talks on the peace process on Friday.