UK Cabinet Office minister Matthew Hancock confirmed that the government will legislate to extend the cut-off date, which was earlier June 7.
Earlier, British Prime Minister David Cameron had exhorted voters to keep trying to register to vote in the June 23 referendum despite the official website having crashed.
The deadline for registrations was to close yesterday but many potential voters were unable to register due to an online glitch, blamed on record demand.
"I'm very clear that people should continue to register today. The Electoral Commission made a statement today urging the government to consider options including extending the deadline.
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"We're working urgently with them to do just that and to make sure those who registered today and who registered last night will be able to vote in the EU referendum," Cameron told the House of Commons during his weekly Prime Minister's Questions.
Users had reported a page displaying the message "504 Gateway Time-out" instead of the online registration form.
"Those registrations will be captured by the system - then we have the legal question about whether captured applications can be eligible for the 23 June," Cabinet Office minister Matthew Hancock told Parliament.
In a statement, the Electoral Commission said it was "vital" that everyone who wants to vote on June 23 is able to do so.
The commission said 226,000 applications to register were received on Monday, the second highest single day's total since electronic registration was introduced in 2014.
More than 45,000 people in the space of less than an hour signed an online petition calling for the extension of the registration deadline.
The deadline for any new or first-time voters to register was set as June 7.
However, most voters already on the electoral rolls have been issued their official polling cards.
Those eligible to cast a vote include British or Irish citizens living in the UK who are 18 or over and citizens of Commonwealth countries who are 18 or over and who can stay in the UK.
Levels of turnout is likely to be crucial to the outcome of the referendum, with both sides trying to mobilise their supporters and to warn people of the consequences of staying at home on the big day.