The assembly, which is controlled by the opposition, says it has the right to name and fire justices under Venezuela’s constitution.
However, the Supreme Court, which is largely made up of pro-government members, has described the move as illegal.
The opposition is stepping up pressure on President Nicolas Maduro to call early elections.
President Maduro has refused and is instead going ahead with plans to form a constituent assembly which would have the power to rewrite the constitution and bypass the National Assembly.
The impasse has left the country in a political crisis and scores of people have died in months of anti-government protests.
Following the National Assembly’s announcement, the government said it would not allow serving judges to be unseated.
Venezuela’s Supreme Court has ordered “civil and military authorities” to carry out “coercive actions” in response to the appointments, but it is unclear what that will entail.
Meanwhile, the opposition Democratic Unity coalition (MUD) has called for protest marches on July 22 from seven points in the capital Caracas to the Supreme Court headquarters.
The opposition says the current justices are illegitimate, having been rushed into their positions shortly before the governing party lost its majority in 2015.
Since the opposition took over the National Assembly last year the court has consistently blocked all bills passed by Congress.
The opposition announced last week that it would appoint new judges and that it would also take the first steps to set up a national unity government. Analysts say such proposals raise the possibility of a parallel state structure.
On July 20, millions of Venezuelans joined a general strike called by the opposition.
At least three people were killed in clashes between police and protesters and there were more than 300 arrests.
Protesters barricaded roads in Caracas and other cities with rubbish and furniture.
The opposition said that 85% of the country joined the strike but President Maduro said its effect was minimal and that its leaders would be arrested.
Meanwhile, Colombia, France, Spain, the US and the EU have urged the Venezuelan government to cancel the vote for a new constituent assembly on July 30.
However, President Nicolas Maduro has rejected the calls.
At least 158 people have died in Spain's worst flooding disaster in generations. On October…
Google has been fined two undecillion (a two followed by 36 zeroes) roubles by a…
Embarking on a home remodel is an exciting journey, promising enhanced comfort, increased property value,…
The US presidential candidates continued to campaign across key swing states on October 20. Footage…
Elon Musk has said he will give away $1 million a day to a registered…
India and Canada have decided to expel their top envoys along with other diplomats as…