President Donald Trump on Monday replaced the acting head of US Immigration and Customs Enforcement, a holdover from Barack Obama's administration, as he battled mounting fallout over his controversial immigration orders.

No reason was given for the decision to replace Daniel Ragsdale, announced barely an hour after Trump fired another Obama appointee, acting attorney general Sally Yates, for breaking rank over the ban on travellers from seven Muslim-majority nations.

Ragsdale's replacement, Thomas Homan, will help "ensure that we enforce our immigration laws in the interior of the United States consistent with the national interest," Homeland Security Secretary John Kelly said in a statement.