MUMBAI, Jan 5 (Reuters) - Indian government bond yields are likely to sustain their upward trajectory in early trading on the last day of the first week of New Year, mirroring U.S. yields following strong economic data that reduced the likelihood of a rate cut.

Market participants also remain cautious ahead of fresh supply of debt through the first weekly central government auction of 2024, during which New Delhi is set to raise 340 billion rupees ($4.08 billion).

The 10-year benchmark bond yield is expected to fluctuate in the 7.20-7.24% range until the debt auction, following its previous close at 7.2208%, a trader with a private bank said.

"There has been no major dovish factor in 2024 so far, and hence, and with supply pressure locally and rising U.S. yields, we could soon see test of 7.25% on the benchmark," the person added.

U.S. yields rose, with the 10-year yield crossing the crucial 4.00% handle, after data showed U.S. labour market remains strong, which tempered expectations of an interest rate cut by the Federal Reserve in March.

The number of Americans filing initial claims for unemployment benefits, known as jobless claims, fell more than expected to 202,000 last week, coming in below estimates of 216,000

While U.S. private employers hired more workers than expected in December and private payrolls increased by 164,000 jobs, the largest monthly increase since August.

Strong data has pushed up the possibility of a pause by the Fed in March, with odds now around 35%, up from around 10% last week, according to CME Fedwatch tool.

Investors will now focus on December non-farm payroll data due after Indian market hours, seeking further cues on the Fed's move in March.

Back home, concerns persist over heavy debt sale in the last quarter. States aim to raise 4.13 trillion rupees, while the central government plans to sell bonds worth 2.37 trillion rupees, taking total supply to around 6.50 trillion rupees. KEY INDICATORS: ** Brent crude futures 0.4% higher at $77.90 per barrel, after easing 0.8% in previous session ** 10-year U.S. Treasury yield at 3.9950%, two-year yield at 4.3804% ** India to sell sovereign bonds worth 340 billion rupees ** RBI to set underwriting fees for 340 billion rupees sovereign bond auction ** RBI to conduct seven-day variable rate repo auction for one trillion rupees ($1 = 83.2580 Indian rupees) (Reporting by Dharamraj Dhutia Editing by)