Trump's administration on Thursday said it would allow game hunters to enter the USA with trophies from Zimbabwe and Zambia.
The Republican chairman of the House Foreign Affairs Committee, Ed Royce, called the administration's original plan the "wrong move at the wrong time".
Earlier this week, it emerged that the Trump administration was lifting a ban on importing hunted elephant trophies.
Public outrage against the administration's original decision to overturn the Obama ban was not limited to the US.
Trump's sons Donald Jr. and Eric are themselves big game hunters.
Groups who have opposed the ban for years have claimed that allowing the hunting of some big game animals can actually contribute to conservation and the overall health of the herd. Both elephants and lions are covered under the Endangered Species Act, a 2015 Fish and Wildlife Service press release announcing lion protections citing the "dramatic decline of lion populations in the wild".
Mr Royce said that when carefully regulated, conservation hunts could help the wildlife population, but "that said, this is the wrong move at the wrong time". "Furthermore, I am not convinced that elephant populations in the area warrant over-concentration measures", Royce said.
The world's largest land mammal, the African elephant has been classified as threatened under the US Endangered Species Act since 1979. "Thank you!" Trump tweeted Friday night.
However, Trump wrote on Twitter Friday evening that the decision had been placed on hold. Where 5 million of the giant pachyderms once roamed African savannahs, there are now just 400,000. "We need immediate federal action to reverse these policies and protect these wonderful animals".