He said President Trump had broadly meant “surveillance and other activities” when he made the allegation in a tweet earlier this month.
Sean Spicer also suggested Donald Trump was not accusing his predecessor specifically.
Meanwhile, the DoJ has asked for more time to provide information about the allegations.
A congressional committee had set a March 13 deadline for the department to provide any evidence of President Trump’s claims but a spokeswoman said it needed “additional time… to determine what if any responsive documents may exist”.
The House Intelligence Committee said it would give the department until March 20 to comply with its request.
In his tweet President Trump said: “Just found out that Obama had my <<wires tapped>> in Trump Tower just before the victory.”
He added: “Is it legal for a sitting President to be <<wire tapping>> a race for president?”
Despite repeated requests, the White House has not given any evidence for the claim.
The White House has instead asked Congress to examine the allegation as part of an investigation into alleged Russian meddling in last year’s election.
A spokesman for Barack Obama has said the accusation is “simply false”.
“The president used the word wiretap in quotes to mean broadly surveillance and other activities,” Sean Spicer told reporters.
“There’s a whole host of tactics that can be used to monitor somebody either through wiretap or other ways,” he added, without giving details.
Sean Spicer also suggested President Trump was referring to the actions of the Obama administration and not accusing the former president directly.
Earlier, Senior White House adviser Kellyanne Conway said she did not have any evidence to back up the wiretapping claim but said there were “many ways to survey each other now”.
“You can survey someone through their phones, certainly through their television sets – any number of ways… microwaves that turn into cameras. We know this is a fact of modern life,” Kellyanne Conway told New Jersey’s Bergen County Record.
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