Sami Abu Zuhri, a spokesman for Hamas said there was no agreement to extend the ceasefire.
Just after 8:00 p.m. three rockets from Gaza were fired at Israel at the Eshkol Regional Council. Rocket sirens sounded in the Shfela area at around 9:45 p.m.
Earlier on Saturday, the government source said Israel was leaning towards extending the truce.
"As far as Israel is concerned, there is no reason to prevent Gaza's people from stocking up on supplies, so long as the military can continue its work against the tunnels. Our war is not against the population," the official said.
Earlier Saturday, Foreign ministers from the United States, Europe and the Middle East called for an extension of the 12-hour ceasefire between Israel and Hamas, French Foreign Minister Laurent Fabius said.
"All of us call on the parties to extend the humanitarian ceasefire that is currently underway," he told reporters after a gathering that included the foreign ministers of Britain, France, Germany, Italy, Qatar, Turkey and the United States.
"All of us want to obtain, as quickly as possible, a durable, negotiated ceasefire that responds both to Israeli needs in terms of security and to Palestinian needs in terms of the social-economic development (of Gaza) and access to the territory of Gaza," Fabius added.
The ministers in Paris, along with senior EU diplomat Pierre Vimont, met on the same day that Israel began a 12-hour ceasefire during which it said it would press on searching for tunnels used by militants. The Islamist group Hamas, which dominates Gaza, said all Palestinian factions would abide by the brief truce.
US Secretary of State John Kerry has been spearheading international efforts to end 19 days of conflict in which 940 Palestinians, many of them civilians, have been killed. The diplomatic push was to continued on Saturday with the Paris meeting of the foreign ministers - including from Qatar and Turkey, which are prime interlocutors with Hamas.