In a phone call from Maduro to Lula, the Brazilian president called for dialogue, stating that it was important to avoid unilateral measures that could escalate the situation.
Tensions between Venezuela and Guyana have been growing in the last few weeks over a long-running border dispute over Esequibo, an area in Guyana where massive discoveries of offshore oil and gas have been made.
Last weekend, voters in Venezuela rejected the International Court of Justice's (ICJ) jurisdiction over the area, backing the creation of a new state.
Lula also suggested that the pro tempore president of the Community of Latin American and Caribbean States (CELAC) -- Ralph Gonsalves, prime minister of Saint Vincent and the Grenadines -- should address the issue.
Lula reiterated that Brazil is ready to support and follow dialog initiatives, reinforcing a joint declaration by South American countries, released earlier this week.
(Reporting by Luana Maria Benedito; Writing by Peter Frontini; Editing by Cynthia Osterman)