"Why are we having all these people from shithole countries come here?"Trump asked lawmakers in reference to Haiti, El Salvador and African countries, the Washington Post reported.
On social media Trump denied using foul language but admitted tough words were spoken.
Democratic Senator Dick Durbin, who was present at the meeting to discuss a bipartisan immigration deal, insisted Trump had repeatedly used "vile and racist" language.
After an emergency session the African group of UN ambassadors said it was "concerned at the continuing and growing trend from the US administration toward Africa and people of African descent to denigrate the continent and people of colour".
Earlier the African Union expressed outrage and demanded an apology.
The comment was "clearly" racist, said Ebba Kalondo, spokeswoman for AU chief Moussa Faki.
"This is even more hurtful given the historical reality of just how many Africans arrived in the United States as slaves and also terribly surprising as the United States remains a massively positive example as just how migration can give birth to a nation," Kalondo said.
Since Trump's alleged remark was not specific about what African countries he was referring to, Botswana's government posted a tweet inquiring whether it was included in the category.
The Botswana Government has also enquired from the US Government through the Ambassador, to clarify if Botswana is regarded as a “shithole” country given that there are Botswana nationals residing in the US, and also that some of Batswana may wish to visit the US.Botswana Government (@BWGovernment) 12 janvier 2018
Botswana's foreign ministry issued a statement calling Trump's comments "irresponsible, reprehensible and racist" and summoned the US ambassador to the country to clarify the situation.
Senegal followed suit with Foreign Minister Sidiki Kaba saying the government "firmly condemned the unacceptable remarks which undermine human dignity, especially of Africa and her diaspora".
The other countries mentioned in the tirade also reacted strongly.
Haiti earthquake annivesary
The government of Haiti, which on Friday marked the eighth anniversary of a devastating earthquake that killed at least 200,000 people, declared itself "outraged and shocked" by the "racist" slur.
Trump denied he ever said "anything derogatory" about the people of Haiti. "Made up by Dems," he tweeted. "I have a wonderful relationship with Haitians!"
Never said anything derogatory about Haitians other than Haiti is, obviously, a very poor and troubled country. Never said “take them out.” Made up by Dems. I have a wonderful relationship with Haitians. Probably should record future meetings - unfortunately, no trust!Donald J. Trump (@realDonaldTrump) 12 janvier 2018
Mia Love, a Utah congresswoman of Haitian descent, called the comments "unkind" and "divisive" .
El Salvador slammed the remarks as "deplorable", especially coming less than a week after Trump announced the end of a special protected status for about 200,000 Salvadoran immigrants, meaning that thousands of families have 18 months to leave or face deportation.
The United Nations slammed the reported remarks as "shocking and shameful" and "racist".
"You cannot dismiss entire countries and continents as 'shitholes' whose entire populations, who are not white, are therefore not welcome," Rupert Colville, spokesman for the UN human rights office, told reporters in Geneva.