Venezuela's constitutional assembly has ordered presidential elections by April 30 as the ruling socialist party seeks to consolidate its grip on power amid a worsening economic crisis.

President Hugo Chavez, the fiery populist who declared a socialist revolution in Venezuela and crusaded against US influence, died on Tuesday at the age of 58 after a nearly two-year bout with cancer.

Venezuelan politicians allied with President Hugo Chavez said they plan to adopt rules that will punish any of their number who abandons the socialist leader.