Kenya's independent Nation Television and KTN networks said early partial returns compiled by their staff at strategic polling stations gave the "no" camp a widening lead in Monday's bitterly contested plebiscite.
With about 380,000 ballots counted, Nation Television said opponents of the draft held a 63 percent to 37 percent lead over supporters of the new charter, backed by President Mwai Kibaki.
Earlier numbers given by both networks had "no" votes outpacing "yes" votes by only 20 percent.
Nation Television said its figures appeared to show a countrywide trend against the new constitution, the first major overhaul to Kenya's founding document since it won independence from Britain in 1963.
The national election board declined to comment on the projections, but released preliminary partial results from three constituencies, showing the "no" side to have carried two and the "yes" one.
"These are provisional results," board chairman Samuel Kivuitu told reporters.
Opponents of the draft document, led by opposition chief Uhuru Kenyatta and Mr Kibaki's influential Roads Minister Raila Odinga, have urged its rejection as it retains sweeping presidential powers.
They accuse Mr Kibaki, who was elected in 2002 on a reform platform, of reneging on promises to address popular demands to devolve significant executive powers to a new prime ministerial position.
The draft creates such a post but endows it with largely ceremonial duties, including presiding over parliament.
Rejection of the draft would be a blow to Mr Kibaki, who has invested heavy political capital in urging adoption of the draft ahead of presidential elections due in 2007.
About 11.6 million Kenyans were eligible to vote in the country's first-ever referendum, held after a bruising campaign marred by violence in which at least eight people were killed and rallies were routinely disrupted.
Polling was largely calm on Monday as long lines of voters queued to cast ballots, although at least two people were injured in brief, isolated clashes in two Nairobi slums, election officials said.
About 50,000 security forces were deployed at polling stations around the country that opened at 7:00 am (0400 GMT) and closed mostly on time at 5:00 pm (1400 GMT).