* U.S. factory orders drop, U.S. services index slips
* Markets closely watching Qatar situation (Updates prices, adds comment)
By Gertrude Chavez-Dreyfuss
NEW YORK, June 5 (Reuters) - U.S. Treasury debt prices fell on Monday in thin trading, as investors booked profits after gains the previous session on a U.S. employment report that underwhelmed expectations and suggested a more cautious Federal Reserve policy beyond June.
Bonds unwound some of last week's gains despite an attack in Britain over the weekend, and the Arab countries' rejection of Qatar on Monday over the latter's alleged support of Islamists and Iran.
Investors also reduced positions ahead of key event risks such as the British elections and European Central Bank monetary policy meeting.
"We had a pretty significant reaction to payrolls, which was a little overdone," said Bruno Braizinha, interest rates strategist at Societe Generale in New York.
"U.S. payrolls took the 10-year yield to the bottom of the range which was 2.17 percent. So we kind of expect a little bit of support when you start hitting the bottom of the range."
Nonfarm payrolls increased 138,000 last month, the Labor Department said. Economists polled by Reuters had forecast a rise of 185,000.
The Qatar situation, on the other hand, is being closely watched by investors, analysts said.
"The issue in Qatar is a little bit supportive for the oil outlook," said Societe's Braizinha.
In general, higher oil prices are positive for prices of Treasuries and negative for yields.
"I would read this conflict with oil producers as more geopolitical and supports a little bit of a rally in oil, with less chances of pressure on the supply side. In this case, it may help Treasuries."
U.S. crude futures on Monday were down 0.5 percent at $47.42 .
U.S. data reports, meanwhile, were mixed, underscoring a trend that has been in place so far this year.
Factory orders fell 0.2 percent in April, its first drop in two months, while an index for the U.S. services sector slipped to 56.9 last month from 57.5 in April, although the employment index was at its highest since July 2015.
Ian Lyngen, head of U.S. rates strategy, at BMO capital Markets in New York did point, however, that the drop in the prices paid component of the U.S. services index to 49.2, from 57.6 in April offers yet another piece of evidence supporting a sustained lower-rate environment.
In late trading, U.S. 10-year Treasuries were last down 4/32 in price, with yields at 2.173 from 2.159 percent late on Friday.
U.S. 30-year bonds fell 10/32 in price, yielding 2.828 percent, compared with Friday's 2.812 percent. (Reporting by Gertrude Chavez-Dreyfuss; Editing by Bernadette Baum and Lisa Shumaker)