(Adds quotes and details)

BEIJING, Aug 11 (Reuters) - U.S. President George W. Bush said on Monday he had expressed grave concern to Russian Prime Minister Vladimir Putin about Russia's "disproportionate response" against Georgia in the South Ossetia conflict.

Bush, in an interview with NBC Sports on his final day at the Beijing Olympics, said that in a discussion with Putin on Friday at the Games he told the Russian leader, "This violence is unacceptable" and urged that all troops return to the August 6 "status quo ante."

"I was very firm with Vladimir Putin. He and I have got a good relationship -- just like I was firm with the Russian president (Dmitry Medvedev)".

"I expressed my grave concern about the disproportionate response of Russia," Bush said. "We strongly condemn bombing outside of South Ossetia."

Bush suggested timing of the South Ossetia conflict had cast a cloud over the Olympic and its ideals. "Here we are trying to promote peace and harmony and we're witnessing a conflict take place," he said.

"Hopefully this will get resolved peacefully," Bush said. "There needs to be international mediation for the South Ossetia issue."

Georgia, a U.S. ally, offered Russia a ceasefire and peace talks after pulling troops back from rebel South Ossetia's capital, and mediators began a mission to end the internationally condemned fighting.

Some fighting still gripped parts of the Caucasus region, however, with Georgia saying early on Monday that there had been fresh bombing by Russia near Tbilisi.

Russia has demanded an unconditional Georgian withdrawal.

The White House had warned Russia on Sunday that military escalation in the Georgia conflict could have a "significant, long-term impact" on relations between Washington and Moscow. (Reporting by Matt Spetalnick; Editing by Jerry Norton)

AlertNet news is provided by