Matvienko headed Russia's delegation at Lula's inauguration ceremony on Sunday.
"The newly elected president confirmed his readiness and interest in restarting Russian-Brazilian relations in terms of increasing trade and economic cooperation, in the scientific sphere, in the technical field, in the sphere of environmental protection, and in a variety of other fields," she said.
Russia and Brazil have the same idea of what the future world should look like based on a fair multipolar order, Matvienko said, adding that both countries have much potential for boosting cooperation.
Russian upper house chief also stressed that Moscow views Brasilia as an important and reliable partner. The countries will celebrate 195 years of diplomatic relations this year, Matvienko noted.
"We very much appreciate the fact that Brazil pursues an independent foreign policy, it does not yield to any outside influences and acts while preserving its sovereignty, its independence and defending its national interests, and in this we are also similar," Matvienko told reporters.
On Saturday, Lula held meetings with the heads of Russian and Ukrainian delegations. Matvientko also met with Cuban Vice President Salvador Valdes Mesa and Speaker of the Mozambican parliament Esperanca Bias on Saturday.