TOKYO (Reuters) -Average base pay for Japanese workers rose in May at its fastest pace in 31 years, data showed on Monday, a sign that bumper pay hikes offered by companies in annual wage negotiations are gradually being passed onto households.

But inflation-adjusted real wages fell for a record 26th straight month as a weakening yen and higher commodity prices pushed up the cost of imports, complicating the Bank of Japan's (BOJ) efforts to normalise monetary policy.

Base pay, or regular pay, rose an average 2.5% in May from a year earlier, the fastest pace since January 1993, around the time when Japan's asset bubble burst.

The rise, which was bigger than a revised 1.6% gain in April, reflected hefty rises in monthly pay agreed by labour and management at annual labour negotiations.

"The data highlights Japan's increasing wage momentum. While real wages continue to fall, they will likely start rising in July," said Yoshimasa Maruyama, chief market economist at SMBC Nikko Securities.

Nominal wages, or the average total cash earnings per worker, grew 1.9% to 297,151 yen ($1,850), accelerating from the previous month's 1.6% gain to mark the highest year-on-year increase in 11 months.

But when adjusted for inflation, wages fell 1.4% in May after a revised 1.2% decline in April.

There were signs that Japan's intensifying labour shortage is leading to broader-based wage rises. Wage hikes at firms with 30 or more employees outpaced inflation for the first time in 26 months, though when very small firms with five or more workers were included, pay hikes still lagged inflation.

Hourly pay for part-time workers rose 4.0% in May from a year earlier, outpacing a 2.7% gain for full-time staff.

($1 = 160.6700 yen)