The current five-day ceasefire was set to expire at midnight local time (2100 GMT).
"Both sides have agreed to a 24-hour ceasefire," the official with the Palestinian delegation in Cairo said.
The official Egyptian MENA news agency later quoted an "official Egyptian statement" confirming the ceasefire's extension.
The negotiations centre on an Egyptian proposal that meets some of the Palestinian demands, such as easing the blockade of Gaza, but defer other stumbling blocks to later negotiations.
Hamas had repeatedly warned it would not extend the ceasefire, pressing for immediate gains that would allow it to claim concessions from Israel after the devastating four-week war in July and August.
But the militant group has come under pressure from both Palestinian president Mahmud Abbas and Egypt, which borders Gaza to the west.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ