After delegations from both sides met, Mr Maduro said: "I am very optimistic".
The Opposition led by Juan Guaido wants a transitional government to replace the Administration of President Nicolas Maduro, and then free elections monitored by global observers.
He commented that his six-point agenda - which Mr Maduro is keeping close to his chest - has "the whole country in mind".
It plunged deeper into political turmoil in January when National Assembly speaker Guaido declared himself acting president in a direct challenge to Maduro's authority.
Venezuela's political crisis continues as Maduro rules the country with an iron fist backed by China and Russian Federation, while Guaido declared himself interim president with support from the United States. I am confident that if we continue working in accordance with this agenda, and if there is no interference from the United States, we will be able to reach some agreements for the sake of Venezuela.
He also called for Venezuela's reincorporation into the Rio Treaty, which could be used to legally justify United States intervention in the nation.
Noting that the first meeting on Monday lasted five hours, Maduro reiterated that Venezuela was "tired of these conflicts", and that it was time for the sides to "reach an agreement and hear each other".
".The process of dialogue with the Venezuelan opposition, with the participation of the Norwegian government, started on the island of Barbados".
In an interview with the Pontifical Foundation "Aid to the Church in Need", Archbishop Baltasar Porras of Merida, apostolic administrator of Caracas and President of Caritas Venezuela, shone the light on the limitations and intimidation perpetrated by the government against Church officials and organizations.
Political scientist Jesus Castillo-Molleda told AFP "the opposition can not defeat the government, neither alone nor with the help of the United States government".
"Iglesias has confirmed his commitment to the dialog process", Rodriguez tweeted.
The opposition, which boycotted the past presidential elections, has refused to acknowledge the reelection of socialist President Nicolas Maduro.
Guaido had recently indicated that he would not participate in any new talks.