"Russia has to be in the majority on this question," the source said.
The comments came as the United States and its key allies lobbied fellow members of the International Atomic Energy Agency (IAEA) to support the resolution in backroom talks at the agency's headquarters in Vienna.
The draft was a softer version of a resolution proposed earlier, the source said in Moscow.
"Russians are huddling together with the Americans to find a compromise in a softer resolution," the source said.
"Iran has to be given room to maneuver so they are not pushed into a corner like North Korea and withdraw from the NPT (nuclear non-proliferation treaty)," the source said.
The negotiations led to the suspension of a key meeting scheduled Thursday of the IAEA's 35-nation board of governors. The session is now expected to be held Friday.
"We're still working behind the scenes to bring as many people on board for the (deadline) resolution as possible," a Western diplomat said.
Iranian Foreign Minister Kamal Kharazi said his government was willing to cooperate, but warned setting a deadline would complicate matters, and again denied Tehran was developing nuclear weapons.
"We are ready to cooperate with the IAEA fully to give them access to files to do an inspection," Kharazi told journalists during a visit to Sarajevo, but warned "putting pressure on Iran will make it more complicated."
Washington claims Tehran is hiding a program to develop atomic weapons.
Russia is building the Islamic state's first nuclear plant in Bushehr, a project that has attracted criticism from Western nations, who fear Tehran may used spent fuel from the plant in a weapons program.
Russia would not call off the project if Iran does not agree to IAEA demands, but would do so if Tehran is found in violation of the agency's norms, the source said.
"Then we'll stop our cooperation immediately," the source said.
The plant was originally due to go online by the end of 2005, but the project has been held up as Russia and Iran negotiate a separate agreement that would oblige Tehran to return the plant's spent fuel back to Russia for storage.