NEW YORK (Reuters) - Interest rates on U.S. 30-year mortgages fell to their lowest in more than three years as benchmark U.S. Treasury yields sagged to their lowest in over four years due to intense demand for low-risk government debt, mortgage finance agency Freddie Mac <FMCC.PK> said on Thursday.

Worries about a slowing global economy and impact from Britain possibly leaving the European Union, known as Brexit, have stoked buying of U.S., German, Japanese, British and Swiss government debt, sending some of their yields to historic lows.

"The 10-year Treasury yield continued its free fall this week as global risks and expectations for the Fed's June meeting drove investors to the safety of government bonds," Sean Becketti, Freddie Mac's chief economist, said in a statement.

The average 30-year mortgage rate fell to 3.54 percent in the week ended June 16, down from 3.60 percent the prior week, Freddie Mac said in its latest weekly survey.

The was the lowest average on 30-year home loan rate since 3.51 percent in the week ended May 16, 2013, according to Freddie Mac data.

On Thursday, benchmark 10-year Treasury yield <US10YT=RR> fell to 1.518 percent, which was its lowest level since February 2012, Reuters data showed.

This week, German Bund 10-year yield <DE10YT=RR> fell below zero for the first time ever.

"Wednesday's Fed decision to once again stand pat on rates, as well as growing anticipation of the U.K.'s upcoming European Union referendum will make it difficult for Treasury yields and -- more importantly -- mortgage rates to substantially rise in the upcoming weeks," Becketti said.

British citizens will vote on June 23 on whether the U.K. should remain in European Union. Two polls on Thursday showed more voters favored Britain to leave the EU.

(Reporting by Richard Leong)