MUMBAI, June 6 (Reuters) - Indian government bond yields were lower in the early session on Thursday as focus shifted to moves in U.S. peers as well as oil prices, with the market digesting Prime Minister Narendra Modi's smaller victory margin for a third term.

India's benchmark 10-year yield was at 7.0183% as of 10:00 a.m. IST, following its previous close of 7.0272%.

"The market has now started looking beyond the election results and we are seeing some reaction to the recent fall in U.S. yields and oil prices," the trader said.

"Only if we see any issue in cabinet formation, we may react again."

U.S. yields continued their decline on weaker-than-expected job growth data ahead of Friday's highly anticipated government employment report for May.

The weak economic data this week has boosted expectations that the U.S. Federal Reserve will deliver two rate cuts of 25 basis points (bps) each this year.

The odds of a rate cut in September have risen to 69%, up from 47% a week earlier, while the Fed is pegged to cut rates by 49 bps in 2024, according to the CME FedWatch tool.

In India, the Modi-led ruling Bharatiya Janata Party won 240 seats, short of a simple majority in the 543-member house, while an alliance led by him won 293 seats, much smaller than what was predicted in the exit polls.

Foreign fund managers said Indian government bonds will continue to attract foreign flows even as a narrower-than-expected victory margin for the Modi-led alliance could prompt a shift in policy.

The central government is set to conduct its fifth buyback for the current financial year later in the day, and the market does not expect strong offers.

The Reserve Bank of India's monetary policy decision is due on Friday, wherein most market participants are anticipating a status quo in rates as well as stance, with a major focus on guidance. (Reporting by Dharamraj Dhutia; Editing by Sohini Goswami)