The two groups said they are "committed to a peaceful transition leading to free and fair elections", the statement said on Monday.
In that vein, the two groups reaffirmed their support to the country's National Assembly and called for full restoration and respect of its powers, as well as the release of political prisoners.
Lima Group is comprised of the Foreign Ministers of Canada, Chile and Peru, while the members of International Contact Group include the High Representative of the European Union (EU) and the Foreign Ministers of Portugal and Uruguay.
The two groups met on Monday "to increase contacts with a view to contribute to a political, peaceful and democratic solution to the Venezuelan crisis", according to the joint statement.
The Lima Group and International Contact Group announced their commitment to continue providing humanitarian aid to Venezuela and neighboring countries amid the migration and humanitarian crises in the region. The two groups also called for increasing aid from international community, according to the statement.
Venezuela has been suffering from a severe political crisis since late January when US-backed opposition leader Juan Guaido proclaimed himself an interim leader in a bid to oust President Nicolas Maduro from power.
Maduro has accused Washington of working with Guaido to orchestrate a coup to take control of Venezuela’s resources.
The United States and over 50 countries recognized Guaido, but Russia, China, Turkey, and numerous other countries have said they recognize constitutionally-elected President Nicolas Maduro as the only legitimate head of state in Venezuela.