Liberal Democrat leadership candidate Nick Clegg has claimed he is ahead of rival Chris Huhne, with about three in five of party members supporting him.
Mr Clegg's camp claim he is ahead in most of the country
A spokeswoman said a poll of 6,000 members showed 60.9% backed Mr Clegg, but there were "two big weeks to go".
But a spokeswoman for Mr Huhne said he was "catching up", with a "lot of undecideds" yet to cast a ballot.
The party says voting has been slower than at this stage in the last leadership contest, in 2006.
The 64,000 Lib Dem members have until Friday, 15 December to make a choice.
A party spokesman told the BBC that about 50% had so far cast their vote, compared with 70% at the same point in the last leadership election.
The Clegg camp says it is ahead in all regions of the UK, except south-central England - which includes Mr Huhne's Eastleigh constituency - where it claims the two candidates are "neck and neck".
The Clegg team says it hase polled 8,000 Lib Dem members, with 60.9% of the 6,000 who responded saying they backed Mr Clegg, the MP for Sheffield Hallam.
A spokeswoman said: "We are very positive but we recognise there are two big weeks to go.
"As a result of that, Nick is trying to keep the momentum going... pushing towards the finishing tape."
A spokeswoman for Mr Huhne said he was doing "better than" polls suggested, adding: "There are a lot of undecideds."
'All to play for'
She also said: "We are running very close behind and catching up. The gap is narrowing.
"Chris is showing that he's not only very good on policy, but also a very good communicator.
"It was always said that Nick was the telegenic performer but I think that Chris has shown that he's good on policy and good on TV and in the media as a whole."
The spokeswoman added: "There's everything to play for."
A YouGov poll of 678 Lib Dem members for Sky News, carried out from 26 to 30 November and published on Saturday, suggested Mr Clegg was ahead with 56% of the vote among all those naming a candidate.
However, the results showed that Mr Huhne, on 44%, was still able to win, with 52% of members yet to cast a ballot.
The new Lib Dem leader will be announced on 18 December. The race was prompted by the resignation of Sir Menzies Campbell in October.