(Adds central bank comments, peso price)
MEXICO CITY, Oct 13 (Reuters) - Mexican policymakers were united in carrying out their third interest rate increase this year to counteract inflationary pressures from a deep slide in the peso, and they warned nervousness about the U.S. election could fuel greater losses.
Central bank board members voted 5-0 to raise the bank's key rate 50 basis points to 4.75 percent in a Sept. 29 decision, minutes from their meeting showed.
Most members thought the central bank faced difficult decisions since economic growth had slowed while inflationary pressures had increased due to the peso's depreciation.
The peso plumbed record lows in September and nearly broke past 20 per dollar as U.S. Republican presidential candidate Donald Trump gained on his Democratic rival Hillary Clinton. The peso bounced back to about 19 per dollar this month as polls showed Clinton increasing her lead over Trump, who has threatend to tax remittances from immigrants to pay for a border wall and unwind free trade with Mexico.
All members agreed they needed to act to anchor inflation expectations and the majority thought it was important to be clear that they would respond "opportunely" to ensure inflation remained under control.
Analysts said the central bank could match any move by the U.S. Federal Reserve to raise rates, though governor Agustin Carstens said earlier this month the bank might not follow the Fed if the outcome of the U.S. election favors Mexico.
Carstens had previously said a Clinton victory would be better for Mexico.
Alberto Ramos, an economist at Goldman Sachs, said in a note that a sharp appreciation of the peso back to around 17 to 18 per dollar could give Mexico room to not follow the Fed.
Mexico's annual inflation rate has crept back from a record low to about the central bank's 3 percent target. The peso was little changed from its levels before the minutes were released, down 0.5 percent at 19.01 per dollar.
One member of the board thought it was important to send the message that the central bank was not defending a certain level in the peso exchange rate, the minutes showed.
Most members noted there was a perception that Mexico's public finances had weakened, but that the 2017 budget proposal, which calls for spending cuts, was a step "in the right direction."
A majority of the board thought that global markets could see greater volatility, particularly if nervousness about the U.S. election deepens.
The central bank said the rate increase, which followed hikes in December, February and June, did not intend to start a cycle of rate increases. (Reporting by Alexandra Alper and Michael O'Boyle; Editing by Bill Trott and Andrew Hay)