ISNA said the three-day trip has been delayed so that it can be better coordinated.
Jalili was to hold talks with Russian President Dmitry Medvedev and Prime Minister Vladimir Putin during the visit, ISNA had reported on Sunday.
Moscow has long been a nuclear partner of Tehran and built Iran's first nuclear power plant in the southern port city of Bushehr, which is not yet operational.
In recent months Medvedev has indicated that Moscow could back fresh sanctions against Iran over its controversial nuclear enrichment programme.
Last week Russian Foreign Minister Lavrov said Moscow does "regret" Iran's refusal to accept the UN-brokered fuel plan.
He noted that the UN Security Council had the capacity to "study further measures on Iran" but did not come out explicitly in support of added sanctions against Tehran.
"Acting with a logic of punishing Iran… is not a sober approach," he said.
Three sets of United Nations Security Council sanctions have already been imposed on Iran over its refusal to suspend uranium enrichment, which lies at the heart of international fears about the nature of its nuclear programme.
Europe and Washington fear that Iran is secretly developing fissile material for nuclear weapons under the cover of its uranium enrichment programme.
But oil-rich Iran insists its nuclear programme is peaceful and solely geared toward generating electricity for its civilian population.
