* Euro sold off after ECB policy action
* Euro near 21-month low vs Swiss franc
* BOJ's Kuroda: dollar strength won't hurt Japanese economy (Updates levels, adds comments)
By Anirban Nag
LONDON, Sept 4 (Reuters) - The euro fell broadly to hit a 14-month low against the dollar on Thursday, after the European Central Bank cut interest rates to ward off the threat of deflation, catching many investors by surprise.
It also fell towards 21-month lows against the Swiss franc of 1.2053 francs, piling on pressure on the Swiss National Bank to respond by either intervening in the foreign exchange market or by imposing negative rates or lifting its three-year old cap from 1.20 francs per euro to 1.25 francs.
The ECB cut its main refinancing rate to 0.05 percent from 0.15 percent. It also lowered the rate on bank overnight deposits to -0.20 percent, which means banks pay to park funds at the central bank, and cut its marginal lending facility - or emergency borrowing rate - to 0.30 percent.
The focus was now on President Mario Draghi's press conference at 1230 GMT. The euro has already fallen a long way, dropping from a high of $1.3701 on July 1 to $1.3036 on Thursday, its lowest since July 2013.
"This has come as a surprise and buys Draghi some time before he puts in a quantitative easing programme in place," said Chris Turner, head of FX strategy at ING. "Draghi has in the past said negative deposit rates are helpful and this will definitely help the euro lower."
Earlier sources told Reuters the ECB was discussing launching a programme of asset-backed security purchases at its ongoing policy meeting. People familiar with the discussions said plans to launch an asset-backed securities (ABS) and covered bond purchase programme worth up to 500 billion euros were on the table at the meeting.
Most analysts had expected it to take at least until next year to make the required changes to the repackaged debt market.
"The euro's downtrend is intact," said Niels Christensen, FX strategist at Nordea.
The dollar was firmer against the yen, rising to a high of 105.10 yen. It has been on the uptrend after Bank of Japan Governor Haruhiko Kuroda said a stronger dollar would not hurt the Japanese economy.
Earlier, the BoJ kept policy unchanged as widely expected, and retained its upbeat view on the economy.
In Europe, the Swedish crown rose against the euro after the Riksbank kept interest rates unchanged at 0.25 percent. It also stuck to its previous forecast that it would start to tighten policy at the end of next year.
In a Reuters poll, the majority also expected no change in the rate path, although some had said there was a chance the Riksbank would push back the timing of its first rate increase.
The euro fell to 9.1620 crowns after the announcement from around 9.2160 crowns, leaving it 0.2 percent lower on the day.
"It is a relief that the Riksbank was not as dovish as some had expected, especially given data of late has been pretty mixed," said Nordea's Christensen. (additional reporting by Masayuki Kitano; Editing by Hugh Lawson/Ruth Pitchford)