The order, by District Judge Derrick Watson in Hawaii, is a fresh legal blow to Mr Trump's immigration crackdown.
The judge said the ban had interpreted a Supreme Court ruling too narrowly.
That decision, made last month, partly reinstated the ban on refugees and travellers from six Muslim-majority countries.
It said only those with "bona fide" family ties would be let into the US.
But the Trump administration decided that did not include grandparents, grandchildren, brothers-in-law, sisters-in-law, uncles, aunts, nephews, nieces and cousins.