The Department of Homeland Security said the vast majority of undocumented immigrants arrested during raids in the first week of February had criminal records.
ICE said some of those arrested will face criminal prosecution in the United States while others will be deported.
On the campaign trail Mr Trump promised to deport three million illegal immigrants.
A spokesperson for ICE on Monday morning attributed the so-called "crackdown" to the natural "ebb and flow" of law enforcement operations.
Immigration and Customs Enforcement arrested 680 people in raids across the USA last week, approximately three-fourths of whom had prior criminal convictions, according to Homeland Security Secretary John Kelly. He called the operations "routine" and consistent with the kind of targeted enforcement operations the agency has conducted for years.
The enforcement activities have sparked protests in many parts of the country, but ICE officials said Monday that the agency has conducted similar national efforts since 2011.
A report released Thursday showed almost one in five immigrants in the USA illegally live in either the Los Angeles or New York City metropolitan areas.
The agency did say that people in the country in violation of federal immigration laws are being evaluated on a case-by-case basis and, "when appropriate, arrested by ICE".
"Those were individuals that are in the country illegally, so they had no documentation or any right to be here in the country", he said.
ICE officials said that of the people arrested during the Southern California raids, 42 had domestic violence convictions, 26 were convicted of drug offenses, 23 for assault and 17 for sex crimes.
"The rash of these recent reports about ICE checkpoints and random sweeps and the like, it's all false, and that's definitely risky and irresponsible", he said.
"Each presidential administration can decide who is a priority for deportation, of course", said Christina Fialho, executive director of the San Francisco-based Community Initiatives for Visiting Immigrants in Confinement.
Western region ICE officials said that 161 immigrants were detained in the Los Angeles area across six counties.
A three-state targeted enforcement operation led by the U.S. Immigration and Customs Enforcement's Enforcement and Removal Operations arrested 190 people, including 19 in SC, according to the Department of Homeland Security.
The raids follow a January 25 executive order in which Trump prioritized the deportation of undocumented individuals who had been convicted of or "charged with any criminal offense", including misdemeanors.