The request went out to 13 of the 14 countries belonging to the regional multilateral bloc which called on him to step down.
On January 4, the group issued a declaration urging Maduro to renounce another term as president. He is set to be sworn in on January 10.
The group alleged Maduro's government has violated democratic norms and that his re-election in May was illegitimate.
Mexico refused to sign the declaration, citing its foreign policy of non-intervention in the internal affairs of other countries.
Maduro claimed the group's real intention was to impose a more business-friendly government on Caracas and access the country's oil and mineral wealth.
The Lima Group, comprising mostly Latin American countries, was formed following the Lima Declaration in the Peruvian capital in 2017 with a proclaimed aim to settle Venezuela's domestic crisis.
