TOKYO (Reuters) - Japan's government is considering compiling a second extra budget sized at less than 1 trillion yen ($12.4 billion) to secure funds for payouts to households hit by the devastating earthquake in March, the Asahi newspaper said on Tuesday.

The government plans to issue deficit-covering bonds to fund the spending, and will compile a third emergency budget in the summer to meet much bigger costs for reconstruction, the paper said without citing sources.

Japan had planned to compile a sizable second extra budget to meet estimated fiscal spending of over 10 trillion yen for reconstruction and payouts to households hit by the quake but it has been struggling to gain support from opposition parties needed to pass related bills through parliament.

For a big second extra budget to be passed, the current parliamentary session, which ends on June 22, would have to be extended for a significant period.

But the government has been wary of doing so as that would mean opposition parties would have longer to grill Prime Minister Naoto Kan and his cabinet over the handling of the nuclear crisis.

To avoid the wrangling from delaying much-needed payouts to households hit by the quake, the government is leaning toward compiling a small second extra budget, the paper said.

The government so far has given out few clues on when the second extra budget will be submitted to parliament, possibly to leave itself flexibility on the timing.

"We have been expecting the need for another extra budget since we enacted the first supplementary budget. As for its timing, we have been considering the need every day and once we confirm the need, we will compile it, submit it and ask parliament to discuss it," Chief Cabinet Secretary Yukio Edano told a news conference on Tuesday.

($1 = 80.795 Japanese Yen)

(Reporting by Leika Kihara and Yoko Nishikawa; Editing by Edwina Gibbs)