The red-shirts have not yet replied to the government on the possibility of a third round of talks to settle their political dispute, Deputy Prime Minister overseeing security Suthep Thaugsuban said on Thursday.
Mr Suthep said all sides need to think about the best interests of the country and rely on reasoning, rather than emotions, to guide their actions.
"I don't know if there will be another round of talks before Saturday, but I personally want further negotiations. Whether it happens depends on the red-shirts.
"We cannot prevent or stop the protesters from gathering [for Saturday's rally]. The group's leaders will decide what their next move will be," he said.
They must decide whether to end the rally so the demonstrators can return home for the week-long Songkran holiday.
"Leaders of the UDD will decide whether they would allow Thai people a breathing space, as the government will continue keeping things in order," he said.
Mr Suthep, who is the peacekeeping operations centre chief, said the centre will continue monitoring the red-shirts' activities to prevent any violence this Saturday.