* Swiss CPI falls 0.1 pct y/y in Sept vs 0.0 pct in Aug
* Weak price pressure supports SNB cap
* Core inflation dips 0.1 pct
ZURICH, Oct 8 Swiss consumer prices fell slightly on an annual basis in September but remained close to zero, data showed on Tuesday, suggesting the Swiss National Bank's cap on the franc is helping to counteract deflationary pressures.
Prices dipped 0.1 percent on the year, in line with the average analyst forecast in a Reuters poll. Prices were up 0.3 percent month-on-month.
The Federal Statistics Office said the monthly rise was due to the end of the summer sales as well as higher prices for oil, vegetables and package tours.
The SNB capped the Swiss franc at 1.20 to the euro two years ago to stave off the threat of deflation and recession after investors piled into the safe-haven currency, pushing it close to parity with the euro.
But a recent string of upbeat economic data and signs of a recovering global economy have led some analysts to question whether the cap may prove increasingly unnecessary as the franc could start to weaken.
At its policy meeting last month, the SNB reaffirmed its commitment to the cap and ultra-low interest rates to fend off deflation, saying there was still a risk of upward pressure on the Swiss franc.
Late last month SNB Chairman Thomas Jordan reiterated that the cap was "indispensable".
Core inflation, which strips out more volatile components such as food and beverages, seasonal products, energy and fuel, slowed by 0.1 percent on an annual basis in September, compared to 0.0 percent in August. (Reporting by Caroline Copley, editing by Gareth Jones)