(Reuters) - Foreigners were net investors in Asian bonds for a second straight month in June, buoyed by expectations of an interest rate cut by the U.S. Federal Reserve amid easing inflation levels and cooling labour market conditions.

Overseas investors acquired a net $3.05 billion worth of bonds in Indonesia, India, Malaysia, South Korea and Thailand last month after about $9.5 billion worth of net purchases in the prior month, data from regulatory authorities and bond market associations showed.

"Recent U.S. inflation data and signs of softening economic activity have kept alive the expectations of Fed rate cuts later in the year," said Khoon Goh, head of Asia research at ANZ.

Data from the U.S. Labor Department showed earlier this month that the unemployment rate increased to a 2-1/2 year high of 4.1% in June, while consumer prices fell by 0.1% last month, supporting views of Fed rate cut.

"This is keeping the risk sentiment positive and benefiting flows into Asia," ANZ's Goh said.

While analysts anticipate the Fed may begin reducing rates in the latter half of the year, they remain uncertain whether Asian banks will match the number and timing of these cuts.

Frances Cheung, an analyst at OCBC Bank, said Asian rates and yields are likely to lag USD rates and yields on a downward move.

"Easing USD rates with more stable Asian rates will partially normalize rates and yield differentials, rendering Asian local currency government bonds more appealing," he said.

In June, Indian bonds received a net $1.79 billion, the biggest monthly foreign inflow in four months as the process of including local debt securities into JPMorgan's widely tracked emerging market debt index began on June 28.

Indian bonds are expected to gain total inflows of about $20 billion in the next 10 months when the country would slowly reach the maximum weighting in the JPMorgan's index.

Meanwhile, Indonesian bonds attracted $2.5 billion worth of overseas capital last month, driven largely by foreign purchases in Bank Indonesia rupiah securities (SRBI).

Cross-border investors, however, exited South Korean, Thai and Malaysian debt to the turn of $757 million, $364 million and $124 million, respectively, following net purchases of $1.07 billion, $423 million and $1.16 billion, respectively in the previous month.