Kasper-Ansermet was to have filled a vacancy created by the departure of German judge Siegfried Blunt - who resigned late last year.
Cambodia is pushing for a seat on the council, UN Security Council, for 2013 and 2014; voting will be held later this year.
HRW also detailed what it views as severe violations of human rights in nations including Cambodia, Indonesia, Malaysia and Vietnam.
The measures are designed to crack down on the sales of pirated U.S. products overseas.
A UN spokesman told VOA Khmer this week the government has an obligation to fill vacant posts at the court.
The letter was delivered to China, France, Russia, the UK and the United States.
Phan Imex was supposed to build 10 buildings to house evicted residents and built eight instead.
The UN appointed a reserve judge to the position, Laurent Kasper-Ansermet, but that appointment has not been confirmed.
Norodom Sihanouk, who is 90, has suffered from cancer, diabetes and hypertension and has made frequently, prolonged trips to China.
A US official said this week that Obama could participate in an Asean summit to be hosted in Cambodia in November.
Witnesses said security guards for the TTY Company opened fire with AK-47s.
Escapees climbed over the walls or jumped the metal gates of the Prey Speu Social Affairs Center Wednesday in full view of observers.