Vanuatu, at the centre of a strategic rivalry between China and Western countries in the region, was plunged into political uncertainty when opposition leader Bob Loughman lodged the no-confidence petition criticising Kalsakau for actions including signing a security pact with Australia.
Vanuatu's Supreme Court ruled on Friday the vote in parliament was won by the opposition party, but stayed action to remove Kalsakau until Monday, to allow for an appeal.
The parliament speaker, Seoule Simeon, lodged an appeal on Monday afternoon, a government spokesman said in a statement on Facebook.
Loughman, who drew Vanuatu closer to China as the previous prime minister, has said the security pact with Australia compromised Vanuatu's "neutral" status and could jeopardise development assistance from China, its biggest external creditor.
China has sent police experts and security equipment to Vanuatu, with a handover ceremony involving Kalsakau taking place on Friday.
Vanuatu's police force said in a statement on Saturday it had "good working relations with all partners - Australia, New Zealand and China".
The United States and its allies are seeking to dissuade Pacific Islands nations from establishing security ties with China, after it signed security and policing pacts with the Solomon Islands.Â