Countries that suffer from major natural disasters always receive offers of aid from around the world. As one would expect, neighboring and allied states are particularly likely to offer aid, and the major contributors tend to be those countries that are also large donors of official development assistance (ODA). But the list also includes countries that one does not normally think of as aid donors.
A Wikipedia page which has been tracking international aid offers to Japan shows that Afghanistan (or rather, the city of Kandahar) has donated $50,000, Albania has offered $100,000, as have Cambodia, Laos and North Korea, which are hardly political allies of Japan (nor, one might think, can they really afford to just give money away like that).
So why might such countries offer disaster relief? It is unlikely that these contributions will make a tangible difference in the relief effort, as money is not the limiting factor in Japan's response. Many of the offers are clearly symbolic, and some donors almost certainly do not expect their offers to be accepted (North Korea, for instance). But there may also be some self-interest involved. It seems plausible that some countries are offering in help in part as a way to express gratitude for receiving Japanese foreign aid in the past and/or in hopes of receiving such aid in the future.
For example, a search of the AidData database (see at the bottom of this posting) shows that Japan has funded about 50 aid projects in East Timor (Timor-Leste) in recent years. Now that country has promised to send 100 people to clear rubble, according to Wikipedia's tally. It seems unlikely that Japan will accept the offer (it would have to house, host, and manage the efforts of 100 people who likely speak no Japanese and have never been to Japan before, at a time when there are almost certainly plenty of local Japanese eager to do the same work). But it will be interesting to see if Japan's aid to Timor-Leste changes at all in coming years.
In fact, there is an earlier natural disaster for which we can look into this a bit more. In the aftermath of hurricane Katrina, about 100 countries and international organizations offered aid to the United States. As with Japan today, Afghanistan and Albania made offers, but they were more generous to the United States, with Afghanistan donating $100,000 and Albania $308,000. Since the scale of devastation and the death toll are far greater in Japan, it is clear that these donations do not reflect the severity of the disaster.
Certainly the United States is much more involved in Afghanistan than Japan is, so Afghanistan's greater largesse is not surprising. But Albania's case is less clear. In fact, according to AidData, US aid to Albania in 2004 (the year before Katrina) was less than half Japan's aid to Albania in 2008, the most recent year for which we have complete data (search results at the bottom of this post). Not only that: U.S. ODA to Albania had declined considerably from 2003 to 2004. It is possible that Albania thought an aid offer might stem any further decline; if so, it seems to have worked, at least temporarily: 2005 (the year of Katrina) and 2006 aid from the US to Albania remained relatively constant. But in 2007 it fell once more, by quite a bit.
These are just two cases out of dozens of ODA recipients that offered assistance to the United States in 2005 or Japan today. As far as I know, nobody has systematically investigated either the determinants of aid offers by ODA recipients, or the impact of such offers on future aid flows, but it seems like an issue well worth investigating further.
• AidData search results: Japanese aid to Timor-Leste in 2007 and 2008
• AidData search results: U.S. aid to Albania, 2003-2007
• AidData search results: Japanese aid to Albania, 2007-2008