The rebels, who are fighting for a communist republic in Nepal, oppose elections proposed for next year by King Gyanendra, who sacked the elected government in October 2002 for "incompetence" and handpicked a new government.
"The old regime (monarchy) is trying to strengthen its hand in the administration by holding the elections at gunpoint by mid-April next year with the help of the army," said the statement.
"The EC is making preparations for the fourth national general elections by the end of March next year by exploiting the Nepalese people," added the statement, which was issued in the name of Maoist Action Team chief Prabha Kiran and Task Force commander Bhusan, who uses only one name.
Although the government headed by Prime Minister Sher Bahadur Deuba is campaigning for the vote, Nepalese civil society, human rights organisations and opposition leaders say polls cannot be held until an agreement is reached with the rebels, who control vast tracts of countryside in the impoverished Himalayan kingdom.
However, EC officials said they had not received any letters from the rebels demanding the resignation of Chief Election Commissioner Keshav Raj Rajbhandari and his three colleagues.
The commissioners held an emergency meeting Friday to discuss the Maoist statement but no details of their deliberations were immediately available.
The EC had recently started discussions with political leaders for the staging of the vote, which is overdue by almost two years, and is gearing to open bureau's in all 75 districts of the kingdom.
It is also in the process of drawing up voters' lists, an EC official said.
The coalition government has already allocated 1.4 billion rupees (20.16 million dollars) for the election, a finance ministry official said.
The latest threat from the Maoists, whose uprising since 1996 has claimed more than 10,000 lives, follows a weeklong blockade of the capital Kathmandu which saw traffic to and from the ancient capital dropping to a trickle and prices of fresh produce rocketing.
The blockade, enforced through fear rather than force, ended Wednesday but the rebels warned they would reimpose it in a month if their demands were not met.
The Maoists, who are inspired by Chinese communist leader Mao Zedong, had said the blockade was to press the government to free colleagues allegedly in detention and to stop classifying the guerrillas as terrorists.