New Zealand named a 15-man squad for the three-Test series against England but said on Monday that Henry Nicholls and Trent Boult are doubts for the first match at Lord's.
Nicholls is still recovering from a right calf injury, with New Zealand naming Michael Bracewell as the 16th man as cover for the top order batsman.
Fast bowler Boult, meanwhile, is expected to arrive in London only on Monday after playing for the Rajasthan Royals in the Indian Premier League (IPL) final in Ahmedabad a day earlier.
Jacob Duffy, Blair Tickner, Rachin Ravindra and Hamish Rutherford were released from the initial 20 player squad.
Skipper Williamson, who left the IPL early to return home for the birth of his second child, has joined up with the squad.
New Zealand are reigning World Test champions. The first Test begins on Thursday against an England side that is now being coached by former New Zealand skipper Brendon McCullum.
NEW ZEALAND SQUAD
Kane Williamson (captain), Tom Blundell (wicketkeeper), Trent Boult, Devon Conway, Colin de Grandhomme, Cam Fletcher (wicketkeeper), Matt Henry, Kyle Jamieson, Tom Latham, Daryl Mitchell, Henry Nicholls, Ajaz Patel, Tim Southee, Neil Wagner, Will Young, Michael Bracewell
