A contract dispute between some players and the board has disrupted a three-week training camp for the triangular series, which will also include Pakistan, with captain Brian Lara among six players to arrive late.
Australian King told a news conference in Barbados: "What we have seen is an improvement from where they were when they arrived for the camp.
"The progression that they have shown me to date has been quite impressive, but they need to be much further."
King, who has called on the expertise of Garfield Sobers at the camp, succeeded Gus Logie
West Indies opener Wavell Hinds said: "He (King) has brought a new sense of motivation to the players. He's very systematic in his approach, he's very disciplined in his approach, and I think the guys are responding very, very well to him."
The West Indies Cricket Board (WICB) and the West Indies Players Assocation (WIPA) have until December 15 to reach a settlement on the contract dispute, which centres on official insistence that players cannot endorse rival companies to the WICB's main sponsor without prior approval.
Both parties have agreed not to make any public statements which could affect a resolution of the dispute but the fact all of the original 25 players named in the training squad did eventually arrive at the camp bodes well.