Sean Spicer said Mr Trump had broadly meant “surveillance and other activities” when he made the allegation in a tweet earlier this month.
He also suggested the president was not accusing his predecessor specifically.
Meanwhile, the justice department has asked for more time to provide information about the allegations.
A congressional committee had set a Monday 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 20 March to comply with its request.
In his tweet Mr 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.
It 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 Mr Obama has said the accusation is “simply false”.
CNN’s Jake Tapper said “we as a nation have had to live in this farce,” referring to the fallout of President Donald Trump’s claims that the Obama administration wiretapped him during the 2016 election.
“The president used the word wiretap in quotes to mean broadly surveillance and other activities,” Mr 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.
Mr Spicer also suggested Mr 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 surveil each other now”.
“You can surveil 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,” she told New Jersey’s Bergen County Record.
Trump wiretap claims: White House softens stance on unproven tweets. WH Sean Spicer said Mr Trump had broadly meant “surveillance and other activities”.