* C$ at C$1.0348 vs US$, or 96.64 U.S. cents * Russia proposes Syria hand over chemical weapons * Proposal could avert a U.S. strike on Syria * Chinese retail sales and factory output data positive * Canada housing starts fall more than expected in August * Bond prices fall across curve By Alastair Sharp TORONTO, Sept 10 (Reuters) - The Canadian dollar hit a three-week high against its U.S. counterpart on Tuesday with investors encouraged by signs that a U.S. military strike on Syria may have been averted, at least for now. U.S. President Barack Obama said on Monday he saw a possible breakthrough in the Syrian crisis after Russia proposed Syria hand over its chemical weapons for destruction, a move that could prevent U.S. military strikes. Still, Obama said he would continue to push a divided Congress to back U.S. action if necessary, saying the threat of force was still required. "As it became more evident that there might be some kind of nonmilitary solution in Syria, that's part of the reason why dollar-Canada has been a little lower," said David Bradley, director of foreign exchange trading at Scotiabank. The Canadian dollar ended the session at C$1.0348 versus the U.S. dollar, or 96.64 U.S. cents, stronger than Monday's session close at C$1.0373, or 96.40 U.S. cents. That was its strongest close against the greenback since Aug 19. The loonie, as Canada's currency is colloquially known, touched its strongest level against the Japanese yen since July 25 on Tuesday. "The markets are very risk-positive today," said Adam Cole, global head of FX strategy for RBC Capital Markets in London. "The markets seem to be worrying a lot less about the Middle East, which has generally given asset markets a positive tone that has spilled over into FX." Meanwhile, encouraging Chinese retail sales and factory output data gave investor sentiment a further boost. The Canadian currency has strengthened against the greenback for three straight sessions, but Scotia's Bradley said his bank has seen strong U.S.-dollar buying interest at around the C$1.03 to C$1.0320 level, suggesting it will be difficult for the loonie to move beyond that. Canadian housing starts fell more than expected in August to hit their lowest since April, hurt primarily by slower condo construction, according to data released on Tuesday that tempered property bubble fears. Prices for Canadian government debt fell across the maturity curve, with the two-year bond slipping 5 Canadian cents to yield 1.311 percent and the benchmark 10-year bond shedding 58 Canadian cents to yield 2.821 percent.