Venezuelan opposition leader and self-declared interim president Juan Guaido is offering amnesty to soldiers who back democracy and reject the current Maduro government.
"We are waiting for you, the soldiers of Venezuela. We are waiting for you and the commitment you have to our constitution," Guaido said at a Sunday news conference.
Opposition followers - some shouting "Soldier friend, you're the only one missing" - handed out leaflets describing the amnesty plans at military and police posts.
Some of the soldiers threw away the paper or tore it up. But many Venezuelan military members have said they and their families are tired of the severe shortages of food and other basics plaguing.
Meanwhile, President Nicolas Maduro insisted Sunday the military is on his side as he watched military exercises using Russian-built rocket-propelled grenades and anti-aircraft machine guns.
"Nobody respects the weak, cowards, traitors. In this world, what's respected is the brave, the courageous, power," Maduro said as he watched bullets from the Russian artillery pound a hillside.
Maduro said he wants peace, but he announced more military exercises next month which he says will be "the most important in the history of Venezuela."
Earlier Sunday, Maduro rejected an ultimatum from a number of European countries that he hold new elections within eight days, or they will formally recognize Guaido as president.
"They should withdraw this ultimatum. No one can give us an ultimatum," Maduro told CNN’s Turkish network.
The United States has condemned last year's Venezuelan election, in which Maduro won another term, as a charade that was neither free or fair.
Two weeks after he was inaugurated for a second term this month, Venezuela's opposition controlled National Assembly declared Maduro's presidency illegitimate. National Assembly leader Guaido invoked the constitution and declared himself interim leader until a new election is held.
'Illegitimate Mafia state'
The United States and many Latin countries recognize Guaido as president.
U.S. Secretary of State Mike Pompeo told members of the U.N. Security Council Saturday to "pick a side" in Venezuela. He called the Maduro regime an "illegitimate Mafia state" and criticized countries who support him, including Russia, China, Iran, and Cuba.
Maduro has backed down on his order to shut down the U.S. embassy in Caracas and the expulsion of all U.S. diplomats.
But Pompeo warned Maduro not to "test the United States on our resolve to protect our people."
National Security Advisor John Bolton tweeted another warning to Maduro against intimidating Guaido or the National Assembly, saying it would be "a grave assault on the rule of law and will be met with a significant response."
Before leaving Panama Sunday, Pope Francis called for a "just and peaceful solution" in Venezuela that respects human rights.
Pope Francis called Sunday for a “just and peaceful solution” to Venezuela's political crisis as he wrapped up a visit to Panama for a World Youth Day rally that was overshadowed by the upheaval unfolding nearby.
Francis refused again to say if the Holy See would recognize opposition leader Juan Guaido in his claim for the presidency, which has been backed by the United States and other regional leaders.
The collapse of world energy prices, corruption, and failed socialist policies have created an economic and humanitarian crisis in oil-rich Venezuela.
Food, fuel, and medicine are in extremely short supply. Inflation is out of control. Millions of Venezuelans have fled the country, and Maduro has shown little tolerance for opposition-led protests
Maduro has blamed his country's woes on the United States, which he accuses of working with the opposition to topple the government.
He has called world leaders who want him gone "Trump sycophants."
Esha Sarai and Margaret Besheer contributed to this report.