* Dollar falls broadly on worries over Trump
* Doubts creeping in over Fed rate hike in June
* Euro buoyed by strong GDP data, euro integration (Updates with afternoon U.S. trading, adds data)
NEW YORK, May 16 (Reuters) - The euro surged more than 1 percent against a broadly weaker dollar on Tuesday, nearly touching $1.11 as it rose to its highest level since Donald Trump was elected U.S. president in November.
The dollar fell after the release of weaker-than-expected data on U.S. housing starts, adding to the economic reports that have missed predictions.
While the dollar made a modest recovery after data showed U.S. manufacturing production recording its largest increase in more than three years, investors again soured on the greenback in later trading.
Data released earlier in the day showed the euro zone economy growing 1.7 percent year-on-year in the first quarter, in line with expectations.
Emmanuel Macron's victory in France's presidential election and growing expectations of further European integration, as he seeks deeper ties with Germany, have also helped bolster the euro, analysts said.
The euro jumped widely, touching its highest level since April 2016 against the yen and its highest level since March 31 versus sterling.
The dollar's sell-off looked like it had further to go, said Boris Schlossberg, managing director of FX strategy at BK Asset Management, given the potential for further political fallout relating to reports that Trump disclosed highly classified information to Russian officials last week.
"It seems like progressively every single day it gets more and more beyond any sense of normal leadership and ultimately that kind of political volatility does translate into economic volatility," Schlossberg said.
Fears are growing among investors that Trump might not serve out his first term, analysts said. Even if he does, they said, there would be too many political distractions for him to push through his economic stimulus program.
The dollar index had risen to 14-year highs earlier this year on the view that Trump's plans for tax cuts and infrastructure spending would boost growth and inflation, but it fell on Tuesday to its lowest level since Nov. 9.
Weaker-than-expected U.S. data is causing traders to wonder whether the U.S. Federal Reserve will fail to raise rates at its policy meeting next month.
Investors are still pricing in around a 74 percent chance of a June hike, but that is down from more than 80 percent last week, according to CME Group's FedWatch tool. (Reporting by Dion Rabouin; Additional reporting by Jemima Kelly in London; Editing by Lisa Von Ahn and Paul Simao)