Having skipped the annual diplomatic gathering, the presidents of Russia and Venezuela instead held their own talks in Moscow on Wednesday.
Putin reiterated his support for Maduro's government, but also highlighted the importance of dialogue between the government and the "opposition forces".
"No doubt we support the dialogue that you, Mr President, and your government are having with the opposition forces," Putin said.
"We believe that any refusal to have dialogue is irrational, harms the country, and only threatens the population's well-being."
The two leaders were scheduled to hold a one-on-one meeting before attending a working lunch with other officials to discuss bilateral cooperation among other issues.
Before leaving Venezuela, Maduro has said his agenda included holding meetings with "important business groups".
No major deals are expected, but Kremlin spokesman Dmitry Peskov said the "implementation of joint projects" will be on the agenda.
Venezuela has been mired in a deep political crisis since January, when opposition leader Juan Guaido declared himself interim president, arguing Maduro's re-election in May 2018 was illegitimate.
Guaido has since been backed by dozens of Western countries and their regional allies.
Russia has been a key ally of Maduro's government during the crisis.
Over the summer, Moscow said it wanted to continue "facilitat[ing] the development of Venezuela's military potential", while the two countries signed an agreement allowing Russia to send military ships to Venezuela.
Russia has also provided support for Venezuela's energy sector - according to a report by the Financial Times, Russia's state-owned company Rosneft was Venezuela's sole supplier of petrol in June.
Meanwhile, Russia has rejected US criticism over its ties with Venezuela and hit out at a number of Washington's anti-Maduro moves, including the opening of a US representative office for Venezuela in Colombia's capital, Bogota.
Earlier in September, Maria Zakharova, spokeswoman for Russia's foreign ministry, called on all states "with influence" to "refrain from unilateral steps and to facilitate inter-Venezuelan talks ... and inclusive dialogue in strict agreement with the constitution".
She also said the US actions were not helping in the efforts to break the political deadlock.
"How can we talk about restoring constitutional order if everyone who is considered legitimate by Washington is being sponsored by Washington," Zakharova said.