A leader of the opposition said the pro-government march had been 'ordered by Cuba'
Venezuela's President Nicolas Maduro has urged the United States to discuss "peace and sovereignty" in a high level commission mediated by the Union of South American Nations (Unasur).
Maduro also asked President Obama not to heed US factions that allegedly want to kill the Venezuelan leader.
Venezuela blames the United States for the anti-government protests that left 28 people dead in the last month.
The US says Venezuela is using it as a scapegoat for its internal problems.
Earlier, thousands of government supporters marched through the Venezuelan capital, Caracas, to thank the country's security forces for their policing of the recent unrest.
Maduro and several military leaders held speeches praising the "civic-military" partnership.
He also proposed the creation of a "high-level commission" to discuss "peace and respect to the sovereignty" in Venezuela.
'HUMBLE BUS DRIVER'
The Venezuelan president said he wanted the head of the National Assembly, Diosdado Cabello, to negotiate with a "high-level officer" of the US administration under the auspices of Unasur.
"President Obama: give peace, and respect, a chance and let's set the foundation for a new type of relations between the US, Venezuela and if possible, Latin America and the Caribbean," he told the crowd in a speech broadcast on radio and TV.
Maduro also warned Obama against agreeing to alleged plans to kill him, put forward by "extremists" in the US administration.
"It would be the worst mistake in your life to authorise the assassination of President Nicolas Maduro and fill [Venezuela] with violence," he told the crowd, adding he was a "humble president and bus driver" who like Obama also had "African grandparents".
The opposition has called for further protests on Sunday against "Cuban repression" in the country and criticised the government's march.
"We know soldiers and officials are against this act ordered by Cuba," Maria Corina Machado, an opposition leader, wrote on Twitter.
On Saturday, there were renewed clashes in the Caracas neighbourhood of Altamira, where protesters have been occupying a square for days.
Earlier, Maduro had vowed to disperse the crowd even if that took the use of force.
On Friday, Venezuela's Foreign Minister Elias Jaua accused US Secretary of State John Kerry of inciting violence and called him a "murderer".
Jaua was reacting to comments by Kerry, who accused Venezuela of waging a "terror campaign against its own people" in its response to protests.
The American Congress is considering sanctions on the oil-rich nation.
The current wave of protests started in the western states of Merida and Tachira at the beginning of February by students demanding more security in the region.
The opposition says it will continue to protest against Venezuela's high inflation, food shortages and violence levels until there is a change of government.