UPDATED 2:45 p.m. ET
(CBS News) -- Presumptive Republican presidential nominee Mitt Romney stepped away from the campaign trail this morning for a private meeting with New York Mayor Michael Bloomberg.
The two met at the Upper East Side offices of Bloomberg's charitable foundation. The former Massachusetts governor, however, said he did not ask for Bloomberg's endorsement.
"The mayor and I had a very nice chat this morning," Romney told reporters later outside a New York City firehouse. Romney and former Mayor Rudy Giuliani were visiting the firefighters to mark the one year anniversary of the death of Osama bin Laden.
Romney said he and Bloomberg discussed the progress New York has made boosting its economy, combating crime and supporting public health.
"You have to look at what New York has done, under this mayor [Giuliani], and under Mayor Bloomberg and say the city is just a remarkable place," Romney said with Giuliani at his side.
A source familiar with the meeting said Romney and Bloomberg also discussed several national issues important to Bloomberg, including immigration policy and the federal budget.
The three-term mayor has so far stayed neutral in the presidential race, even as both President Obama and now Romney have reached out to the billionaire businessman turned politician. A registered independent, Bloomberg was once considered a possible 2012 presidential candidate himself.
For Romney, a Bloomberg endorsement could be a double-edged sword. Bloomberg's background as a successful businessman - his financial information and media company Bloomberg LP made him a billionaire - would boost Romney's argument that he is the candidate best able to manage the economy and help Romney woo independent voters.
However Bloomberg has also been an outspoken national advocate for several issues that are anathema to conservatives, such as climate change and gun control laws. Bloomberg is also less conservative than Romney on social issues. In February, when the Susan G. Komen Foundation announced it was withdrawing funding from Planned Parenthood, Bloomberg stepped in with a donation pledge of up to $250,000. The Komen Foundation later reversed its decision. Romney has said as president he would end federal funding for Planned Parenthood.
Romney made multiple appearances in New York today. Besides meeting with Bloomberg and visiting local firefighters, Romney also attended the memorial service for legendary CBS News correspondent Mike Wallace.