The US Secretary of State for her part said Iran's failure to agree to a UN-brokered nuclear fuel exchange deal aimed at breaking the impasse was seen as "a turning point" by other major powers involved in talks.
"It is clear that it is not possible to wait for ever," Lavrov said after the talks in London, where both he and Clinton are to attend an international conference on Afghanistan on Thursday.
The comments are the latest sign of apparent growing Russian frustration over Iran's refusal to agree a deal.
"We are disappointed that Iran has not reacted constructively to the proposals" offered by world powers, he said in remarks broadcast on Russian state television.
Clinton added: "Increasingly our partners around the world see Iran's refusal to agree… as a turning point."
A US official suggested it was now apparent more pressure would have to be applied to move the process forward.
"We've reached the reluctant conclusion that we need to go further on the pressure track," said the official.
Lavrov "said that we have the same vision, the same goal", the official added.
Britain, China, France, Germany, Russia and the United States have been negotiating with Tehran over its nuclear programme amid concerns that it is secretly developing fissile material for nuclear weapons — which Iran denies.
Under the UN plan, Iran would hand over most of its stocks of low-enriched uranium in return for the supply by France and Russia of nuclear fuel enriched to the higher level required for a Tehran research reactor.
Russia, a veto-wielding permanent member of the United Nations Security Council, is one of the few major powers to have close relations with Iran.
The United States has over the last months actively looked for explicit backing from Moscow for tougher sanctions against Tehran should the Islamic Republic continue with its defiance.
An official with Clinton said earlier that Washington was "working on the possible elements of a (UN) Security Council resolution and to take stock of existing Security Council resolutions and what additional actions can be taken to implement those."
Russia has traditionally been wary of further Security Council sanctions against Iran, but Lavrov indicated moves for additional measures were already afoot in New York.
"Our partners are already talking about the necessity of discussing additional steps at the Security Council so that we can move forward to the goals set by the international community," he said.
Moscow's capacity to provide technical help for the Iranian nuclear drive is seen by some analysts as giving it an unmatched power of leverage in Tehran.
Russia is building Iran's first nuclear power plant in the southern city of Bushehr and the facility is due to finally come on line this year.
The West suspects Tehran is trying to develop an atomic bomb under cover of its civilian nuclear energy programme. Russia has said there is no evidence to support these accusations.
