"I have of course read about violations of [US] voters' rights but no one is going to question the results of the American election,” he told journalists.
"Naturally, we will continue to work with this administration when it is renewed,” he added.
Lavrov said Secretary of State Hillary Clinton was unlikely to stay on in that role, and had told him as much during a recent meeting on the sidelines of the APEC summit in Vladivostok.
Russia and the US have "plenty of common interests,” he said, but there are also "differences on some issues.”
"Nevertheless, we will be ready to go as far as the US administration is ready to go in deepening our cooperation,” Lavrov said.
World leaders congratulated US President Barack Obama on Wednesday on his return to the White House for a second presidential term after an election victory that was far from certain.
But congratulations from Moscow were muted, with President Vladimir Putin preferring to wait and send a telegram rather than call Obama in the hours after his election victory over Republican challenger Mitt Romney. Putin’s spokesman said, however, that the Kremlin was, "in general, extremely positive” about Obama’s election victory.