* Dec core CPI falls 1.3 pct yr/yr, smaller drop than in Nov
* Index stripping out energy costs falls faster
* Industrial output rises on firm exports to Asia (Adds details, background)
By Stanley White and Tetsushi Kajimoto
TOKYO, Jan 29 (Reuters) - Japan's core consumer prices fell from a year earlier for the 10th straight month in December, meaning the government will likely keep pushing the Bank of Japan to ease monetary policy more.
The pace of decline slowed from November as the effect of oil price falls faded, while factory output continued to rise on the back of solid demand for Japanese goods in Asia.
But the so-called "core-core" consumer price index, which strips out the effect of energy costs, fell at a faster pace in December in a sign of anemic demand. That will worry policymakers who fear a return to recession ahead of elections in the summer.
"The pace of decline in the core-core CPI accelerated and we should take this to mean that deflation remains a problem," said Yasuo Yamamoto, senior economist at Mizuho Research Institute.
"The BOJ needs to continue its easy monetary policy. For the government's part, they may need to consider another stimulus package, as the economy is stagnating."
But Prime Minister Yukio Hatoyama's government has little room to boost spending further as the national debt is now almost twice as big as the country's annual gross domestic product. Credit ratings agency Standard and Poor's this week warned that it may cut the country's rating.
Parliament will soon debate the government's record budget for the year starting in April and the threat of a credit ratings downgrade by Standard and Poor's means
The core CPI, which includes oil products but excludes volatile prices of fresh fruit, vegetables and seafood, fell 1.3 percent in December from a year earlier, matching market forecasts. It was smaller than a 1.7 percent drop in November.
The so-called core-core inflation index, similar to the core index used in the United States, fell 1.2 percent in December from a year earlier after a 1.0 percent drop in November.
Industrial output rose 2.2 percent in December as manufacturers continued to benefit from a strong economic recovery in Asia, although the increase was smaller than the 2.5 percent forecast by economists.
The BOJ forecast on Tuesday prices would fall less than earlier thought but remained open to further policy easing in the face of renewed government calls for more support for a fragile economic recovery.
The central bank, under pressure from the government, has toughened its stance on deflation and in early December decided to offer commercial banks more short-term funds.
The government and BOJ agree stimulating demand is essential to conquering deflation, but the BOJ has already committed to keeping rates at a very low level and the government's support for households could take a long time to have an impact.