Colombia’s president, Juan Manuel Santos, has announced he is extending a ceasefire with the country’s largest rebel movement in an attempt to give more time to efforts to save a peace deal rejected by voters.

Santos said in a televised address that he was extending by two months the ceasefire with the Revolutionary Armed Forces of Colombia (Farc) until 31 December.

He made the announcement after meeting students who have been organising demonstrations across the country to demand the accord be implemented immediately despite it being rejected in a referendum.

“Let it be clear: this isn’t an ultimatum or deadline,” Santos said, adding that he hoped to have an agreement before the end of the year. He said the lives of soldiers and guerrillas depended on warfare not resuming. “Time is conspiring against peace and life,” he said.

Santos, winner of this year’s Nobel peace prize, is engaged in three-way talks with the Farc and the opposition to find ways to adjust the accord to win broader support.

The former president Alvaro Uribe, who led opposition to the peace agreement, is demanding significant changes such as stiffer penalties for rebels who committed war crimes.

Meanwhile, the rebels, who would be spared prison sentences under the accord, are insisting they will not go back to the drawing board and throw out more than four years of arduous negotiations with the government.