New Zealand captain Kane Williamson has confirmed that his hamstring is fine but elbow might still need "a little bit of time" to get back to 100%. The elbow complaint has been a long-standing one for Williamson, forcing him to miss the ODI series at home against Bangladesh, the start of the first leg of IPL 2021 in India and the Edgbaston Test against England.

After leading New Zealand to World Test Championship glory, Williamson continued to manage his elbow as he withdrew from the Hundred, where he was supposed to turn out for the Birmingham Phoenix.

"The hamstring is minor, it's progressing nicely, so not too many concerns and we've still got plenty of time," Williamson said, speaking from New Zealand's base in Dubai. "So, yeah, hopefully in the next sort of few days or so, I'm taking basically full part in the training. So, it's all good.

"The elbow - it has just been a bit of a slow-burner. Yeah, it has been quite frustrating for a long period of time. However, it has definitely improved a bit over the last two months I've had after the World Test Championship. On rehab, it has definitely seemed to move forward, which is refreshing, but still a little bit of time to get back to a 100 [%], but it's definitely better."

Williamson explained that he has been feeling some discomfort while gripping the bat and extending the elbow, but was pleased with his overall rehab in months that followed the WTC final against India.

"Basically just gripping and then extending," Williamson said. "So, which you do a lot of obviously [while] batting and it has been frustrating certainly when it was at its worst. But the harder you grip and further you extend, the more it seems to be quite disruptive. Like I said there's been a lot of improvement over the last three months, which is good. That has really been the focus and I'm at the stage where I'm largely about to get through with some comfort and it's nice to be able to focus a bit more on the cricketing side of things rather than having constant negotiations with physios."

Williamson's niggly elbow - and the fitness of the other players - will be put to test when New Zealand play their last four group-stage games in seven days across the three venues in Dubai, Sharjah and Abu Dhabi. Three of those matches will have afternoon starts (2pm local time).

"Recovering will be a big part of that," Williamson said. "The temperatures are getting a little bit better and being here nice and early - it allows the guys to acclimatise a little bit [to the conditions] and get a little bit more comfortable in these sorts of temperatures. Those day-offs after the game, especially when it's as dense as that, will be really important so that guys can be back up and be as fresh as possible going into the following game."

Williamson has already had a taste of the slow, low UAE pitches, having been Sunrisers Hyderabad's second-highest run getter in the second half of the tournament, behind Jason Roy, with 138 runs in six innings at an average of 27.60 and strike rate of 102.98. Williamson was wary of the conditions, reckoning they could change at the forthcoming World Cup.

"They've varied a lot actually," Williamson said. "Even a lot compared to what we experienced last summer when we had the whole tournament here [the UAE] and in previous years when we've played here as well. Something to be aware of; something certainly to prepare for and try and make those adjustments as quickly as possible and get comfortable with what realistic expectations are and what competitive totals are because it has not unfolded in that traditional T20 style at times.

"But then we've had other days, in the IPL when we turned up to Abu Dhabi, the wicket looked very similar, but there was sort of an 80-run difference in what was perhaps a par total. It is really adjusting to what's in front of you as quickly as possible and trusting in that judgement."

After the T20 World Cup in the UAE, New Zealand will tour India to launch their defence of the World Test Championship and three T20Is. Williamson urged New Zealand to focus on the job at hand - and their collective progress.

"I mean there's a lot of challenges in front of us," he said. "I mean any tournament, any World Cup is always tough, particularly the T20 World Cup. There are match-winners in every team and anybody can truly beat anybody and for us, we want to continue the path of growth and improve as a side and make those adjustments. There are very little promises in this game, but we want to continue to get better as a side and hope that holds us in good stead. That'll be our focus and that will be important for us in this tournament.

"And then the focus will change, it will be on India and [we will] try and get a bit of clarity around what we might expect in some of those conditions, which can also vary quite a lot. Be nice and clear how we want to operate there. As a side, it's always a challenge [when] you have a number of different world events, but ultimately in terms of the bigger picture, you want to keep evolving and moving forward as a team and that's where you try and put your energy."