He has also been published by multiple media outlets, including the Seattle Times.
"Otherwise they should shut up and support the men and women on the front lines", he added.
Members of Arizona congressional delegation did not return requests for comment on the comments Tuesday.
Critics say the agency is too heavy-handed in enforcement operations, including arresting undocumented immigrants in the USA who do not have criminal records.
Kelly added that DHS will continue to "investigate marijuana's illegal pathways along the network into the USA, its distribution within the homeland, and will arrest those involved in the drug trade according to federal law".
Some members of Congress fear the White House will propose significant cuts to other DHS components, such as the Transportation Security Administration and Coast Guard, to pay for immigration enforcement priorities. "We want to get the law breakers off our streets, and out of the country, for the good of our communities".
"Make no mistake - we are a nation under attack", Kelly said at George Washington University in his first major public speech since taking the helm of the Department of Homeland Security (DHS). 'These are the cases we know about'.
The threat of terrorism is as high today in the United States as it was the morning of 9/11, the nation's top homeland security official said in a blunt warning, with ongoing federal terrorism probes in every state. ". These numbers are lower because we've shown that we're serious about border security and enforcing our immigration laws".
Without naming former President Barack Obama, he said that the drivers of the morale issues that have plagued his department were "stopped on January 20". He said the relationship between the Mexican and US governments is now "in good shape".
General Kelly stressed his interest on getting to the root of America's drug problems over merely cracking down on dealers, users, addiction, and crime in the USA, things more in USAG Session's wheelhouse.
Since Trump signed a travel ban banning entry for people from seven Muslim-majority countries and cracked down on deportation of undocumented immigrants, protests have erupted in cities all over the US.
He said he and President Trump have made a decision to free up agents to enforce the laws as written, and he said he and his department won't apologize for that.
Despite gains against human smuggling, Kelly admitted the department still grapples with a growing drug problem in America. The DHS chief said cocaine seizures have risen almost 40% since October, along with an uptick in heroin and methamphetamine seizures.
Kelly conceded that he does not think the department can "arrest their way out of this".