US intelligence agencies under Mr Obama reportedly monitored Mrs Merkel's phone, sparking an angry response.
But both Republican and Democratic congressional leaders have said they do not believe Mr Trump was wiretapped.
Mr Trump and Mrs Merkel have discussed key issues including Nato and trade.
Her visit had been scheduled for Tuesday but was postponed due to a snowstorm.
Mr Trump made his wire-tapping jibe in a joint press conference with Mrs Merkel. She gave a quizzical look.
He was also asked about a comment by White House press secretary Sean Spicer that the UK's GCHQ spy agency had carried out wiretapping on Mr Trump during the US election campaign.
Media captionTrump's wiretap saga explained in two minutes
Mr Trump said Mr Spicer had been quoting a comment on Fox TV. The president said he had not offered an opinion on it, adding: "You shouldn't be talking to me, you should be talking to Fox."
Fox later read out a statement on air, saying: "Fox News knows of no evidence of any kind that the now president of the United States was surveilled at any time in any way, full stop."
GCHQ rejected the allegations against it as "nonsense" and Downing Street says it has been assured the US will not repeat the claims.
The US president was also asked if he regretted any of his regular tweets. He said "very seldom", adding that it was a way to "get round the media when it doesn't tell the truth".
The body language was at times awkward. In an earlier photo opportunity in the White House, Mrs Merkel asked him quietly: "Do you want a handshake?" He looked forwards with his hands clasped and did not reply.
Analysis: BBC North American reporter Anthony Zurcher
The US president and the German chancellor were standing on the same stage, but it often seemed they inhabited different political universes.
Donald Trump, once again, focused on the issues that he campaigned on - issues, he is quick to remind reporters, that won him the presidency. He was quick to talk about "fair" trade, immigration control, military strength and manufacturing jobs.
Angela Merkel, on the other hand, focused on the benefits of globalism, openness to refugees and the need to negotiate a "safe and secure solution for Ukraine".
Leaders find their way into politics "on different pathways", as Mrs Merkel pointed out, and that was clearly the case at the White House on Friday afternoon.
The fast-talking Mrs Merkel, steeped in policy details, stood in stark contrast to the staccato Mr Trump, who once again railed against unfair treatment at the hands of foreign trade negotiators and the domestic media.
Somehow these two very different individuals will have to find a way to work together on issues of global importance. This face-to-face meeting - complete with non-handshake and awkward body language - will likely prove to be only a tentative first step.
Nato and trade were key points of discussion for the two leaders.
Mr Trump reiterated his strong support for the alliance, but also "the need for our Nato allies to pay their fair share for the cost of defence".
Germany is among many Nato members that do not meet the benchmark 2% of GDP to be spent on defence.
Mrs Merkel said Germany was committed to increasing its defence spending.
Media captionTrump meets Merkel: The biggest difference between the US and Germany
On trade, Mr Trump bristled at a suggestion that he believed in "isolationist" policies. He told the reporter asking the question: "I don't know what newspaper you're reading, but I guess that would be an example of fake news."
He added: "I believe a policy of trade should be a fair trade. And the United States has been treated very, very unfairly by many countries over the years and that's going to stop."
Mrs Merkel, who is travelling with top executives from German companies Siemens, Schaeffler and BMW, said she hoped the US and the EU could resume talks on removing barriers to bilateral trade.
More on Trump and Merkel:
The two leaders certainly have hugely contrasting ideas and leadership styles.
BBC Berlin correspondent Jenny Hill says he is flamboyant, impetuous and prone to rhetoric, while she is reserved, pragmatic and lingers over decisions.
In January, Mr Trump said the German chancellor had made "a catastrophic mistake" by allowing hundreds of thousands of refugees and migrants into Germany.
For her part Mrs Merkel has criticised President Trump's controversial travel ban that targets the citizens of several mainly Muslim countries.
Immigration was clearly one of the issues on which the leaders had, as Mrs Merkel put it, "an exchange of views".
He said immigration was "a privilege not a right" and that "safety of our citizens must come first", whereas she said: "Refugees have to be given the opportunity to shape their own lives."
Our correspondent says Angela Merkel needs to walk a diplomatic tightrope. She has to build a working relationship with Mr Trump without appearing to sacrifice her own values or disappoint those keen to cast her as the West's last defender of those democratic ideals.
This first meeting comes as she prepares for an election battle later in the year, seeking a fourth term as chancellor.
Media captionWhat do you make of Mr Trump's demeanour?
'Awkward few moments' - Body language expert Professor Geoffrey Beattie of Edge Hill University
This is an awkward few moments in front of the cameras. The most significant aspect of this particular 'interaction' is the actual lack of any interaction between the two. President Trump uses a 'steeple' gesture - fingertips together, but pointing forward. Steeple gestures are usually associated with extreme confidence. This one suggests the cameras (to which he is pointing) are the most important thing in the room, indeed more important than Mrs Merkel.
As is often the case with Donald Trump, it is nonverbal communication primarily about power and status. Mrs Merkel's body language reinforces rather than contradicts this message. She leans towards him, attentive to his every signal, but he pays her no visual attention.
At one point, Mrs Merkel makes an involuntary movement as if psychologically prepared to shake his hand, but Mr Trump makes no such movement. He is in control of this interaction and he knows it.
Source : BBC
