US President Donald Trump has called for an "expedited" hearing of his controversial travel ban targeting six Muslim-majority countries, currently before the Supreme Court, saying the justice department should seek a "much tougher version".

In a series of tweets on early Monday morning, Trump also said the US is already "extreme vetting" travellers coming into the country for safety reasons.

Trump referred to his executive order barring visitors from six Muslim-majority countries, which is currently held up in the courts, as a "travel ban", a characterisation his administration had previously rejected.

An initial executive order was drafted and signed in January, but it was later blocked by courts and prompted large protests at airports in cities and towns across the country.

A revised version of the executive order was issued in March.

Last week, the Trump administration appealed to have overturned decisions by the lower court to block the revised ban to the Supreme Court. 

In late May, an appeals court in the US state of Virginia refused to reinstate Trump's temporary travel ban, stating it was rooted in "intolerance".

The 4th Circuit Court of Appeals ruled 10 to three against Trump's travel ban, and indicated opponents of Trump were likely to succeed at trial in showing the policy violates US constitutional prohibitions on religious discrimination.

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The decision, written by Chief Judge Roger Gregory, described Trump's executive order as using "vague words of national security, but in context drips with religious intolerance, animus, and discrimination".

Gregory quoted statements by Trump during his campaign calling for a "Muslim ban", and wrote that a reasonable observer would likely conclude the order's "primary purpose is to exclude persons from the United States on the basis of their religious beliefs".

Trump's administration argued the court should not look beyond the text of the executive order, which does not mention religion.

The countries were not chosen because they are predominantly Muslim, but because they present "terrorism" risks, the administration claimed.

Source: News agencies