The statement may have dismayed Merkel who said that the "success of Germans has always been one where the German success is one side of the coin and the other side of the coin has been European unity and European integration".
"As far as wiretapping, I guess, by this past administration, at least we have something in common, perhaps", Trump said, drawing laughter.
"But this has to be done by looking at the refugees as well, giving them opportunities to shape their own lives and where they are", Merkel said on Friday.
Trump said trade agreements have led to greater trade deficits. But he did defend Spicer's slander of GCHQ.
However, former foreign secretary Sir Malcolm Rifkind said it was not enough to promise not to repeat the allegation. Which is why was she there in the first place?
Mr Trump refused to apologise for the accusation. Saturday morning, Trump claimed on Twitter the two had a "GREAT" meeting before berating Germany, claiming they owe the US money for defense, which is not how North Atlantic Treaty Organisation works.
Trump also said he is a strong supporter of North Atlantic Treaty Organisation, but stressed that member countries need to "pay their fair share for the cost of defense".
On trade, Mr Trump bristled at a suggestion that he believed in "isolationist" policies.
Only the USA and four other members now reach the benchmark of spending 2 percent of GDP on defense. "We are trying to address the areas where we disagree....and find a compromise".More news: Tillerson Tells State Department Employees Budget Cut Reflects New Priorities
Her visit was scheduled for Tuesday but had to be postponed due to a snowstorm.
Mr Trump earlier greeted the long-serving stateswoman at the White House with a handshake before they began talks in the Oval Office. Later, both leaders told reporters their meeting was very good.
Trump's tweet from his Florida resort, where he is spending the weekend, came the day after his first meeting with Germany's leader. However, Ms Merkel did ask if he would like a handshake - an offer Mr Trump appeared to loftily ignore.
That appeared to be far from the case on Friday, when the veteran German leader arrived hoping to reverse a chill in relations after Trump criticized her during his campaign previous year, saying her decision to allow refugees into Germany was a "catastrophic mistake" and suggesting she was "ruining Germany".
German chancellor said that there wasn't enough time to discuss economic policy in detail yet.
Merkel has criticized Trump over his travel ban against Muslim-majority countries, though also voiced a desire to work with him after his election.
Asked about his unsubstantiated claims that the Obama administration had placed him under surveillance late previous year, Trump made reference to the disclosure in 2013 that the National Security Agency had been tapping Merkel's mobile phone.