From next month, working parents in England will be entitled to 30 hours of free childcare for three- and four-year-olds, up from the current 15 hours.
But there have been concerns that the government has not set aside enough money to pay for it, and the government has conceded that there have been "glitches" with a website set up to allow parents to register.
In response to a letter sent by treasury select committee chair Nicky Morgan earlier this month asking about the performance of the website, HMRC's chief executive and permanent secretary John Thompson said he is "very sorry that some parents" have experienced problems with the service, adding that they are working to improve things.
Labour has now called on the government to reassure parents that the website will be able to cope, ahead of the extended offer coming into effect next week.
Tracy Brabin, Labour's shadow early years minister, said: "The government is clearly failing working parents.
"Ministers should have taken their responsibility to deliver an application system that works much more seriously.
"This policy is supposed to be implemented in just over a week and yet thousands of parents' claims are still stuck on waiting lists because of a ‘technical issue'.
"Parents and providers urgently need assurances that the scheme will be able to cope."
In his letter to Morgan, Thompson said that where parents have had difficulty accessing the service because of technical issues, HMRC is issuing 30 hours free childcare codes manually, and is paying parents the government top-up for tax-free childcare.
Morgan has said the treasury select committee will question HMRC representatives on the technical issues with the childcare service website when they are called to give evidence in the autumn.
"Whilst it is welcome that HMRC has made significant improvements to the website since it was launched in April, thousands of parents are still unable to apply for the childcare to which they are entitled in the way that the government has envisaged," she said. "Clearly, further improvements are still required."
Neil Leitch, chief executive of the Pre-school Learning Alliance, said: "We recognise that HMRC are working hard to rectify the problems with the website, but the fact remains that thousands of parents and childcare providers have been adversely affected by these glitches.
"While we welcome Nicky Morgan's intervention on this matter, it really is a case of too-little-too-late. Both 30 hours ‘free childcare' and tax-free childcare were key Conservative manifesto promises, which the government seem wholly unprepared to deliver.
"The very least we expected was investment in an IT system that parents are able to use, and through which childcare providers are able to receive the payments that their businesses rely on."
Purnima Tanuku, chief executive of National Day Nurseries Association, said: "The response from HMRC to Nicky Morgan has highlighted all the technical difficulties that many parents are facing when they try to access their eligibility codes through this website.
"The most important aspect of this for parents is that they receive their codes in time for their child to start their funded place from September. No-one who is eligible should lose out on their entitlement.
"We are pleased that HMRC is working to resolve these issues swiftly.
"But the government must also understand that nurseries are spending valuable time and resources trying to resolve these issues for their parents - at a time when the government funding does not even cover their costs of delivering childcare.
"Not only should parents be compensated for these problems, but nurseries should be fully supported to deliver these hours and paid for their admin time."