By Ian Dunt
Barack Obama called David Cameron this evening to congratulate him on the birth of his youngest baby.
Samantha Cameron is still recovering in Cornwall with her husband. The couple decided to name the girl Florence Rose Endellion.
"President Obama called the prime minister earlier today to offer his congratulations to the prime minister and Mrs Cameron on the birth of their daughter," a Downing Street spokesperson said.
"There was also a brief discussion on the Middle East."
The Camerons have been congratulated by figures across the political spectrum since the surprise birth of their daughter yesterday, including by deputy prime minister Nick Clegg.
"He sounds over the moon. I'm really thrilled," Mr Clegg told reporters.
"Miriam [Clegg] and I are so happy for David and Samantha, as I think everyone is."
The Liberal Democrat leader will have to keep "holding the fort" a little longer, with Mr Cameron expected to extended his holiday following the birth of his new daughter.
"I hope they get the time out to enjoy the new arrival to the family in peace," Mr Clegg said.
The girl, who arrived a few weeks prematurely, was born in Cornwall yesterday to a visibly euphoric David and Samantha Cameron.
But questions were immediately raised about how the birth would affect constitutional arrangements over the summer.
Mr Cameron had been expected to be on paternity leave during a UN summit in New York next month. Nick Clegg was scheduled to step out from the Liberal Democrat conference early to attend in his place.
Downing Street officials confirmed today that they would stick to that arrangement despite the change in circumstances.
The prime minister was also set to miss the TUC conference because of paternity leave. It now appears he will still miss the conference.
Analysts suspected that Mr Cameron was secretly rather pleased to be able to use his paternity leave as a watertight excuse for missing the union conference, where he was sure to receive a hostile reception from delegates.
The decision to stick to the previous plan on Mr Clegg's visit to the UN suggests the deputy prime minister thought he could consolidate his position with the party best by being seen on the world stage rather than by remaining at conference, where concerns about Lib Dem cooperation with the Tories are likely to be publicaly expressed.
The deputy prime minister will address the assembly about international development - a subject close to many Lib Dem hearts.
Officials will be hoping that his prominent role on such a prestigious stage will demonstrate to disaffected Liberal Democrats the benefits of entering a coalition government.
Under employment law fathers are entitled to two weeks paternity leave and Mr Cameron is under some pressure to take the full allotment, given his previous pledge to make the UK "the most family-friendly country in Europe". He may chose to do so in bits and pieces, however.