He also started talking with Mexican President Enrique Peña Nieto about who would pay for the wall, sparking an argument that caused Peña Nieto to cancel a planned meeting with Trump.
General Kelly added that it would not simply be just a wall but a "layered" defence to stop potential migrants crossing illegally into the United States.
It was Kelly's first visit to the border since being tapped to lead one of the largest government agencies in the country.
Kelly also addressed previous media reports that hinted that he did not know about Trump's executive order that temporarily banned refugees from entering the US until the president signed it last Friday.
"Mr Trump is not loved by everyone in America and I think this very rapid succession of decisions, I don't think the American public is really all that used to people making decisions", he said.
McCain told CNN's Manu Raju that Mexico paying for the wall is "not a viable option".
Dems boycott committee vote, but Republicans unanimously approve Trump's EPA pick
Murray said in a statement Wednesday she opposes any rule change that would allow nominees to be "jammed through". Committee chairman John Barrasso accused the absent Democrats of engaging in delay and obstruction.
"I saw the initial couple of cuts on them probably on Tuesday maybe Thursday, knew it was coming soon and then it came, ' Kelly said, replying "not at all" when asked if he was 'blindsided" by its release.
"Like Americans, Mexicans have pride", Mayor Darling said.
Secretary Kelly also told Fox News what his wife said when President Trump offered him the role in the administration.
But Democrats are likely to resist anything the Republicans put forward.
"The point is, [Trump] has a promise that he made to the American people to secure our border".
But former Ohio Democratic Rep. Dennis Kucinich, a Fox News contributor, said Congress has a responsibility to review the request. "We don't want taxpayers to have to take it in the neck".
After an global backlash caused by President Trump barring travel into the U.S. from seven majority-Muslim countries, General Kelly defended his boss.
- Kim Kardashian's stolen jewellery was allegedly melted down and sold
- Al-Shabab, Kenya trade claims in morning attack in Somalia
- UK: Trump state visit puts Queen in 'difficult position'
- Liverpool will use Private Jet to Rush Player Back vs Chelsea
- Reptile Dysfunction: Portland Woman Gets Python Stuck In Her Ear
- Lakers forward, Sudanese refugee Luol Deng responds to President Trump's travel ban
- Attorneys: Briles drops libel suit against Baylor officials
- Trump Administration Pushes For Dakota Access Pipeline To Move Forward03:38
- AFCON 2017: Ghana Black Stars depart for Franceville
- Volkswagen shrugs off emissions scandal to become world's biggest carmaker