Venezuelan President Nicolas Maduro called Sunday for local elections, but not an early presidential election, which millions of protesters have been demanding.
In his weekly television address, Maduro endorsed voting later this year at the mayoral and gubernatorial level and also called for talks to resume with the opposition. He asked Pope Francis to "keep accompanying” the political dialogue.
Another large anti-government demonstration is planned for Monday after tense protests erupted across the country in the beginning of this month that left at least 20 people dead.
Saturday, protesters clad in white held peaceful, silent marches across Venezuela to pay respects to those who have died.
Human rights groups have said more than 1,000 people were detained during recent disturbances and over 700 are still in detention.
Demonstrators have been calling for presidential elections due next year to be held earlier and for Maduro to step down. The government has ruled out voting this year at the presidential level.
The opposition blames the government for the unraveling of Venezuela's once-booming economy, which has left the country with shortages of food, medicine and basic goods.
The near-daily protests were sparked by an attempt of the Supreme Court to take over the powers of the opposition-dominated Congress.
Venezuela's government has also barred opposition leader Henrique Capriles - twice a major presidential candidate - from running for office for 15 years.
The 44-year-old Capriles, currently governor of Miranda state, which surrounds Caracas, is one of the most recognizable leaders behind the protest movement that has been roiling the country for three weeks.