Howard Wolfson called Trump's address "presidential" and a "home run."
"That will be for a later date," he said at a joint press conference with the Mexican president.
Trump also acknowledged weapon smuggling as a problem.
He called ending illegal immigration a "shared objective."
Oakland has a population of over 400,000 people.
The Trump camp has booked time in Florida, North Carolina, Ohio, Pennsylvania and Michigan.
OPINION | Successful candidates are ones who tell the better story
Trump is not an official representative of the American government.
Trump is set to address the media following his meeting with Mexico's president.
The ads will air in battleground states Ohio, Florida, North Carolina and Nevada.