President Goodluck Jonathan participated directly in the discussions, they said. Late-night wrangling ended earlier in the day without a compromise.
Oil labor unions will not shut down production of crude as planned, according to union sources who did not want to be named because of the sensitivity of the talks.
Last week, a major oil union, Petroleum and Natural Gas Senior Staff Association of Nigeria, threatened to halt production Sunday in solidarity with protesters if the two sides don't reach an agreement.
A move to halt production would reverberate on the global market -- Nigeria is the world's eighth-largest crude exporter.
Throngs of protesters have taken to the streets to demand government accountability and a return of fuel subsidies that ended on January 1, a move that doubled gas prices and sent the cost of other goods skyrocketing.
Scattered protests escalated into a national strike that started Monday, paralyzing the nation of more than 160 million people.
Union leaders called for a temporary suspension to the national strikes for the weekend to allow protesters to stock up on food and water, but said they would resume Monday if the subsidies are not reinstated.
"The whole labor movement will return to strike Monday but negotiations are continuing," said Elijah Okubu, president of NUPENG, another oil workers' union. "Negotiation is the hallmark of industrial relations."
Nigerians flocked to stores Sunday to buy basic necessities amid uncertainty on how long protests will last once they resume. Long lines snaked around gas stations, as crowds flooded markets to buy food.
Demonstrations started as an outcry against the removal of fuel subsidies and grew into anger against government corruption. Nigerians consider the subsidies one of the few benefits of living in an oil-producing nation that has little infrastructure, high unemployment and intermittent electricity.
The protests -- dubbed "Occupy Nigeria" -- have galvanized the continent's most populous nation.
Nigerians accuse their leaders of corruption and misusing oil revenues in a country where most citizens battle grinding poverty.
The government has said the removal will free up billions this year to boost the economy and improve the country's infrastructure.
But there is a widespread lack of trust in the government to provide the infrastructure; Nigeria is regularly ranked among the most corrupt countries in the world.
Finance Minister Ngozi Okonjo-Iweala said Nigerians should not let the past determine the future. She said the goal now is to regain the citizens' trust and move forward.
"They cannot say because of mistakes in the past the country should not move forward," she said.
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