Thames Valley Police said it is "determined" to end a siege at a house in Oxfordshire "as soon as possible".
Local Policing Area commander Superintendent Christian Bunt said:
It is believed the man is armed, although no indication has been given that he wishes to harm the children.
We are doing all we can and our officers are determined to bring this situation to a close as soon as is possible.
More top news
The new Duke and Duchess of Sussex attended a garden party in Buckingham Palace - their first public engagement as a married couple.
The Tottenham striker was confirmed as Three Lions skipper by manager Gareth Southgate during a team meeting at St George's Park on Monday.
The company said the 'loss-making' Tesco Direct web portal will cease trading on July 9.