(Adds comments on monetary policy, background)
MEXICO CITY, June 18 (Reuters) - Most of Mexico's central bankers think that economic growth remains sluggish and see no signs a weak peso has fueled inflation, suggesting they could hold interest rates steady in the coming months.
Central Bank board members voted 5 to 0 at their June 4 meeting to hold their benchmark rate at a record low of 3.0 percent, minutes showed on Thursday.
Most policymakers said there was still slack in the economy that would help contain price pressures, the minutes showed. That backs analysts' expectations the bank is unlikely to raise interest rates before the U.S. Federal Reserve does so.
But all policymakers said they faced a dilemma, given that the economy was sluggish and inflation was low but that they may need to raise interest rates due to expectations about the Fed that could affect the peso and the local inflation outlook.
All members said they would move to adjust borrowing costs if inflation expectations deteriorated sharply. Two members voiced some arguments that could justify raising interest rates ahead of the Fed.
However, most thought that, as long as inflation expectations remained anchored, raising interest rates before the Fed would have more costs than benefits, given the slow inertia of the economy.
Most policymakers said inflation was tame and would remain below 3 percent for the rest of the year despite a deep slump in the peso since late last year amid bets that higher U.S. rates will push investors to dump emerging market assets.
Data this month showed Mexico's annual inflation rate cooled in May to a record low of 2.88 percent, below the central bank's 3 percent target, in a sign that there has been no widespread consumer price pressures from the peso's losses.
Mexico's peso has bounced back some from a record low this month. All policymakers said international volatility could hit Mexican markets again.
Latin America's No. 2 economy grew at its slowest pace in over a year in the first quarter, hit by flagging oil revenue and weak U.S. growth.
Last year, economists expected Mexico could grow nearly 4 percent this year on bets that an opening of its energy sector would boost growth. But a sharp drop in oil prices has dampened hopes for a tide of investment.
Analysts now see the economy growing around 2.7 percent this year. (Reporting by Michael O'Boyle Editing by W Simon)