An appeal bid by two anti-China lawmakers against their disqualification from Hong Kong's parliament was rejected Monday, as the activists declared "war" on the authorities.

Baggio Leung and Yau Wai-ching are part of a new movement calling for semi-autonomous Hong Kong to split from China as concerns grow that Beijing is cracking down on freedoms in the city.

The pair deliberately misread their oaths of office, inserted expletives and draped themselves with "Hong Kong is not China" flags during a swearing-in ceremony in October.

They were then disqualified from retaking their oaths by Hong Kong's high court, after an intervention by Beijing.

Hong Kong's court of appeal rejected an attempt to overthrow the disqualification in November. On Monday it also rejected their bid seeking leave to take their case to the city's court of final appeal -- Hong Kong's highest court.

Speaking outside the court, Leung, 30, told reporters: "This is the beginning of a war."

Justice Maggie Poon based her Monday ruling on a special "interpretation" of the city's constitution by Beijing in November that effectively prevented Yau and Baggio from taking up their seats because of the way they took the oath.

The latest judgment said Beijing's interpretation was "binding on the courts" in Hong Kong with the local and national systems "being within one country".

An appeal would only be granted if it had "reasonable prospects of success" even if the case was of great public interest, the ruling said.

The court also ordered the pair to pay costs of HK$167,851 ($21,600) each.

Leung said the pair would continue to push their case. Under Hong Kong law, they can seek a hearing directly with the court of final appeal, without leave from the lower courts.

The independence movement has started to gain traction since the failure of mass pro-democracy rallies in 2014 to win political reform.

Leung and Yau were voted into parliament in citywide polls in September which saw several rebel candidates take seats for the first time, advocating either independence or self-determination for Hong Kong.

The Hong Kong government has launched a legal bid to unseat four more elected lawmakers, sparking protests and accusations from the opposition camp that they are being subjected to a witch hunt.

The four are not stridently pro-independence, but among them high-profile pro-democracy activist Nathan Law and teacher Lau Siu-lai have advocated self-determination for Hong Kong.