It follows a National Audit Office (NAO) report, which revealed that the rollout will cost at least ?92m less than BT had originally said.
The government said that the spare cash would be ploughed back into offering fast broadband to more remote areas.
BT said that the claim - made by MPs on the Public Accounts Committee (PAC) - was "bizarre".
PAC told the BBC it questioned why BT had told the committee it would cost so much more.
"Although it's reassuring that the cost to the public purse could end up being ?92m (25%) less than what BT had originally forecast in its bid, I worry that this does not stack up with what BT told my committee in 2013 - that it factors in a contingency of between 5% and 8%, which might not get spent, a much smaller proportion than 25%," Margaret Hodge, chair of the PAC, told the BBC.
"It is very concerning that it looks like BT could have abused its dominant position in the market by vastly overestimating forecast costs in the first place when it put in its original bid, and we also have broader concerns about whether the deal represents value for money."
In response BT said that its initial cost estimates were "based on our initial view of how much it would cost to deploy fibre in rural areas".
"We have come in under budget in several areas which is good news for the taxpayer as we only charge for the costs we incur, not those we first forecast. The savings can now be reinvested to take fibre to additional areas."
"The suggestion we inflated those costs is bizarre as by doing so we would have hindered our chances of winning the work."
"The NAO report this week confirmed our costs were 20% below those others would have charged in a sample area, so we are clearly delivering excellent value for money."Rural disadvantage
The distribution of broadband is overseen by Broadband Delivery UK (BDUK), part of the Department for Culture, Media and Sport (DCMS).
The report found "significantly lower" costs than listed in BT's financial model for the first phase of the scheme.
"As at September 2014, BT's total reported capital spend on phase 1 of the programme was ?142 million (38%) under the estimated price, including work in progress not yet invoiced," the NAO said.
Taking into account possible further costs, BT would still have spent "approximately ?92m less", the report concludes.
This sum will be ploughed back into rural rollouts, the DCMS said.
"The savings realised so far, along with with projected future savings, will be reinvested in extending the current rollout plans."
Several reports have found that rural businesses, schools and homes are at a significant disadvantage because of poor broadband.
Bringing faster services to remote areas has proved to be highly controversial.
Questions have been raised about the time it has taken the government to start the rollout and whether the plans are ambitious enough.
Last year the Public Accounts Committee accused the government of mismanaging the project, and said BT released "wildly inaccurate" estimates of costs.
Mrs Hodge said at the time: "The taxpayer has been ripped off, with ?1.2bn going to the shareholders of BT."Ultra-fast broadband
BT's status as the only operator providing rural broadband could actually be one of the reasons for costs being cut, said Andrew Ferguson, editor of the ThinkBroadband news site.
"It is interesting that a chunk of the savings are down to the fact that only one supplier won all the contracts, increasing the economies of scale, at the expense of competition," he said.
Mike Kiely, a former adviser to BDUK, has long argued that BT's estimates of the cost of distributing broadband to rural areas were far too high.
He felt vindicated by the findings, saying: "Thirty-eight per cent excess costs have been confirmed in the cost models used to calculate the milestone payments. Those monies - and there will be more - need to be used to extend the fibre rollout further."
He and others argue that BT should think about offering even faster broadband - by taking so-called "fibre-to-the-premise" technology, which offers significantly higher speeds than BT's preferred technology of "fibre-to-the-cabinet".
BT hopes to deliver speeds of up to 500Mbps (megabits per second) to homes via an innovative technology known as G.fast.
"We believe G.fast is the key to unlocking ultrafast speeds and we are prepared to upgrade large parts of our network should the pilots prove successful," chief executive Gavin Patterson said.
The firm expects to offer initial speeds of a few hundred megabits per second to millions of homes and businesses by 2020.