Boris Johnson is expected to take a short period of paternity leave later this year, a Downing Street spokesman has said.
Mr Johnson's fiancee Carrie Symonds gave birth in a London hospital early Wednesday morning - a spokeswoman for the couple said both mother and baby were doing well.
It is understood Mr Johnson was present throughout the delivery, with the news that he would be absent from Prime Minister's Questions coming shortly before the birth was announced.
A Downing Street spokesman told a Westminster briefing: "I do expect the Prime Minister to take a short period of paternity leave later in the year, rather than now."
The spokesman confirmed the family will live in Downing Street but was unable to provide details of the weight, timing, nature or location of the birth.
New fathers are entitled to up to two weeks of statutory paternity leave.
However, while this leave cannot start before the child’s arrival, it must end within 56 days, or eight weeks, of the birth.
This statutory leave is paid at £151.20 per week, or 90 per cent of average weekly earnings, depending on which is lower.
Expectant fathers must give at least 15 weeks' notice to their employer.
Some couples are entitled to take 50 weeks of shared parental leave in the first year after a birth or adoption, although the eligibility criteria are narrower than for the statutory benefit.
Mr Johnson and Ms Symonds's son is the third baby born to a serving prime minister in recent history. Former prime ministers Tony Blair and David Cameron both took paternity leave after the births of their children while in office.
Mr Johnson has previously indicated that it was likely he would take paternity leave. When asked in early March whether he intended to take time off, Mr Johnson said: "The answer is almost certainly, yes."
The PM later added: "I can’t remember what the question was." Since then, the coronavirus outbreak has progressed significantly.
The number of people who have died in hospital after testing positive for Covid-19 has now reached more than 20,000, while the number of daily deaths has reached its highest so far in early April.
The nationwide lockdown imposed on March 23 is set to be reviewed early next month.
The Prime Minister only returned to Downing Street on Monday, having been treated for coronavirus symptoms in intensive care, and spending time recovering in Chequers.
Mr Johnson tested positive for Covid-19 on March 27 - Ms Symonds later suffered symptoms of the virus.
Foreign Secretary Dominic Raab deputised for the Prime Minister while he was receiving treatment and recovering from the virus. Mr Raab stood in for Mr Johnson at Wednesday's Prime Minister's Questions.
If Mr Johnson does take paternity leave, it is not known whether Mr Raab will resume the position deputising for the PM.
Tony Blair attracted praise for his decision to take two weeks of paternity leave after his wife Cherie gave birth to son Leo in 2000 - Leo was the first baby born to a serving prime minister in 152 years.
Conservative prime minister David Cameron and his wife Samantha welcomed daughter Florence Rose Endellion Cameron in 2010.
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