The rebels want to push government forces out of the eastern regions of Donetsk and Luhansk and are trying to capture the key town of Debaltseve.
Dozens of people including civilians were killed in clashes and artillery fire at the weekend.
Attempts to agree a truce failed when rebel negotiators did not turn up.
A fragile ceasefire agreed in early September in the Belarusian capital, Minsk, collapsed last month when rebels stepped up their offensive on several Ukrainian positions and seized Donetsk airport.
Rebels were accused of carrying out an artillery attack on the south-eastern Ukrainian port city of Mariupol which left 30 civilians dead.
Ukrainian government forces have also been blamed for deadly attacks on Donetsk city and other rebel-held areas last month in which dozens of civilians were killed.
“Mobilisation will start in 11 days’ time,” Mr Zakharchenko, the head of the self-proclaimed Donetsk People’s Republic, told Donetsk news agency.
However, the rebels’ ability to raise large numbers of forces is unclear.
The first question that springs to mind, after Alexander Zakharchenko’s mobilisation announcement, is where all these fighters will come from. The territory of the self-declared Donetsk and Luhansk People’s Republics had a pre-war population of a few million, and it is unclear how many people remain.
So it could be political bluster – an attempt to match rhetorically the Ukrainian government’s own mobilisation plans. However, it should be noted that Kiev plans to carry this out over the course of the year and not, like the separatists, in little more than a week.
But Mr Zakharchenko’s statement could indicate something much more serious. The rebels have already threatened a full-scale offensive, promising to push to the borders of the Donetsk and Luhansk regions, and possibly beyond. This most likely would require a huge number of forces. Many in Kiev are now concerned the Donetsk leader may be preparing the ground for major intervention from Ukraine’s neighbour, Russia.
Christopher Miller, a journalist based near Debaltseve, told the BBC he thought it was “very unlikely” the rebels would be able to mobilise 100,000 men.
It was more likely that rebel leaders were attempting to use the announcement as “a disguise to bring in more Russian volunteers”, he said.
Ukraine has alleged the rebels are being helped by as many as 9,000 Russian servicemen, a claim the government in Moscow denies.
Russian Foreign Minister Sergei Lavrov meanwhile accused the Ukrainian government of taking “a course towards a military solution to the conflict”.
Mr Zakharchenko emphasised that recruits to separatist forces would be voluntary, Donetsk news agency said.
“It is a reserve force which will definitely be able to resist any attack,” he was quoted as saying.
They would have a month’s combat training with the aim of providing five additional brigades, the Donetsk agency reports.
Ukraine’s government has also announced plans to boost its forces in the east, and mobilise 200,000 troops in 2015.
Tanks and other heavy military vehicles were seen heading towards Debaltseve on Sunday in an attempt to bolster government defences in the town.
Hundreds of civilians were moved out of the town by Ukrainian government forces amid reports that the separatists had reached the outskirts.
A Canadian journalist who is in the conflict zone said the rebels had been involved in a tough battle as they tried to encircle Debaltseve.
“It’s been quite surprising to hear how many have said they are experiencing significant losses and many of their fellow fighters have been killed,” Kristina Jovanovski told the BBC World Service Newsday programme. “That’s not something that you often hear.”
Military officials in Kiev said on Monday that five soldiers had been killed in the past 24 hours, although separatists said the number was more than 20. Thirteen civilians were killed in separatist-held areas during the same period, rebel sources said.
The latest fatalities mean at least 60 people have been killed during a weekend of heavy violence in the eastern regions of Donetsk and Luhansk.
Overall, more than 5,000 people have been killed and some 1.2 million have fled their homes since last April, when the rebels seized a big swathe of Luhansk and Donetsk regions, following Russia’s annexation of Crimea.