The leader of forces in eastern Libya has ordered them to march on the capital Tripoli, the base of the internationally recognised government.
Khalifa Haftar's order to the self-styled Libyan National Army came as UN chief Antonio Guterres was in Tripoli.
Armed groups from the western city of Misrata, which back the government, have vowed to stop any advance.
Libya has been riven by violence and division since long-time ruler Muammar Gaddafi was deposed and killed in 2011.
What reaction has there been?
Mr Guterres, the US and European nations have all called for calm.
Speaking to reporters in Tripoli, Mr Guterres said he was making a "strong appeal to stop... the escalation".
The UN Security Council will meet on Friday to discuss the situation following a request from the UK, reports said.
The US, UK, France, Italy and the United Arab Emirates (UAE) issued a joint statement appealing for calm.
"At this sensitive moment in Libya's transition, military posturing and threats of unilateral action only risk propelling Libya back toward chaos," the statement, issued by the US state department, said.
"We strongly believe that there is no military solution to the Libya conflict," the governments added.
The UN had been planning to hold a conference in Libya later this month for talks over ending the country's long-running crisis.
What is happening on the ground?
After Gen Haftar's announcement, his forces moved towards the capital from several directions, one of his spokesmen said.
There were conflicting reports that Gen Haftar's forces had entered the town of Gharyan, 100km (60 miles) south of Tripoli.
The Libyan National Army (LNA) says it has secured Gharyan and moved on. However it said two of its soldiers had been wounded in clashes in a nearby area.
A Gharyan official told AFP that there were "ongoing efforts to avoid a confrontation" between rival fighters in the town.
The UN-backed government in Tripoli said it had put its forces on high alert.
Meanwhile residents in Misrata said armed groups from the city had begun moving towards the Libyan capital, Reuters reported.
I am deeply concerned by the military movement taking place in Libya and the risk of confrontation. There is no military solution. Only intra-Libyan dialogue can solve Libyan problems. I call for calm and restraint as I prepare to meet the Libyan leaders in the country.— António Guterres (@antonioguterres) April 4, 2019
The offensive comes after Gen Haftar's forces seized parts of the south of the country earlier in the year.
Who is General Haftar?
A former army officer, he helped Colonel Gaddafi seize power in 1969 before falling out with him and going into exile in the US. He returned in 2011 after the uprising against Gaddafi began and became a rebel commander.
In December Gen Haftar met Prime Minister Fayez al-Serraj from the UN-backed government at a conference but refused to attend official talks.
Gen Haftar has received backing from Egypt and the UAE, who see him as tough on Islamists.
He visited Saudi Arabia last week, where he met King Salman and Crown Prince Mohammed bin Salman for talks.