"But it's old thinking to say that if we disagree in one area that we shouldn't work on something else that is of overwhelming importance."
Clinton and Lavrov's meeting follows anger in Moscow over the Nato alliance's month-long military exercises in Georgia which began on Wednesday, a move Russia has called an "overt provocation".
Georgia has in turn accused Russia of backing a mutiny at one of its military bases.
US and Russian negotiators recently began negotiating to replace the 1991 Strategic Arms Reduction Treaty (Start), which expires this year.
The talks were launched after the first meeting between Obama and Dmitry Medvedev, the Russian president, last month.
Disagreements between the US and Russia also remain over how to deal with Iran's nuclear programme and the US's missile system plans in Europe.
Later on Thursday Lavrov will also hold talks with Barack Obama, the US president.