But they underscored the extent of the split.
One issue was whether Iran has the right to enrich uranium, a possible step towards weapons development.
Lavrov said that Iran, as it insists, has that right. "In accordance with the Nuclear Nonproliferation Treaty [NPT] and in accordance with the [International Atomic Energy Agency] IAEA charter, each member country of the NPT has such a right [to enrich uranium]," he said.
But Rice said being a signatory to the treaty is not just about rights. Iran must recognize its obligations, too, she said. "This is therefore not an issue of rights; this is an issue of whether or not the [nuclear] fuel cycle can be trusted in Iran," she said
There was also disagreement over how to resolve the issue. It centers on U.S. accusations that Iran is secretly developing nuclear weapons, charges Iran denies.
The United States would like Iran to return to negotiations with European countries over its nuclear activities. If it doesn't, Washington wants Tehran referred to the UN Security Council for possible sanctions.
Rice's visit was seen as an effort to drum up Russian support for those efforts. But Lavrov said he saw no grounds for taking the issue beyond the UN's nuclear watchdog, the IAEA.
"We think the current situation allows us to actively work over Iran through the IAEA," Lavrov said. "The IAEA inspectors are permanently based in Iran; they report to the IAEA board [of governors] on the progress of their work and in keeping with the present structure we do not see any grounds for passing this issue to other organizations."
Last month, Russia abstained from a key vote at the IAEA. The board passed a resolution that said Iran was in "noncompliance" with nuclear proliferation safeguards.
IAEA board members meet against next month when they are expected to decide whether to send the case to the UN Security Council.
Correspondents say Lavrov's comments mean there's no sign, publicly at least, that Moscow is shifting to back the U.S. policy.
For news and analysis of Iran's nuclear program, see RFE/RL's "Iran's Nuclear Program" microsite.