Brazil was one of several countries that attended Ukraine's so-called "peace summit" in Switzerland last month, an event Russia was not invited to attend.
"I ... sent my aide, Celso Amorim, to Ukraine to talk with [Volodymyr] Zelensky and to Russia to talk with [President Vladimir] Putin, to see if there was a breakthrough that would allow for peace talks to begin," Lula told Radio Princesa.
The Brazilian president said that his country would never be part to the Ukrainian conflict and reiterated that it could end at the negotiating table.
In May, Brazil and China issued a joint proposal for peace in Ukraine which called for an international peace conference "that is recognized by both Russia and Ukraine, with equal participation of all parties as well as fair discussion of all peace plans."
President Vladimir Putin said in June that Russia would immediately cease fire and begin negotiations with Ukraine after Kiev withdrew troops from Russia-controlled territories and officially abandoned its plans to join NATO.
Putin described Ukraine's NATO ambition as a direct threat to the national security and insisted that Kiev's non-aligned status was extremely important for future peace efforts.
Ukrainian President Zelensky rejected Moscow's proposal as an ultimatum. His presidential term expired on May 20, but he postponed the election, citing martial law.