(Adds central bank comments)
MEXICO CITY, June 1 (Reuters) - Mexico's central bank board agreed unanimously they needed to raise interest rates last month to anchor inflation expectations, but they were divided on whether they were close to finishing a cycle of increases, minutes of the meeting showed on Thursday.
The Banco de Mexico voted 4-0 in its May 18 decision, with board member Roberto del Cueto absent, to raise its benchmark rate by 25 basis points to 6.75 percent, the highest since March 2009, in a move that surprised most analysts.
Mexico's central bank has raised interest rates by 375 basis points since the end of 2015 to limit the inflationary impact of a deep peso slump.
According to the minutes, two board members thought the bank was nearly done raising rates, barring any big new shocks to prices, while the two other members thought policymakers should wait to make sure inflation is converging again to the bank's 3 percent target before deciding if they are done.
Three of the members thought the balance of risks to inflation had lessened modestly since their previous meeting in late March.
Mexico's annual inflation rate rose more than expected in early May to 6.17 percent, the fastest pace in more than eight years.
Minutes showed most policymakers thought inflation would begin to fall by later this year and converge back to the 3 percent target by the end of 2018.
A deep slump in the peso last year pushed prices higher, but the currency has recovered this year as concerns have waned that the United States may impose tariffs on Mexican-made goods.
Most board members thought the balance of risks for growth had a downward bias, but they said there was "the perception that the probability that some of the most extreme negative risks materialize has diminished."
U.S. President Donald Trump's administration has softened its rhetoric on trade with Mexico and agreed to renegotiate the North American Free Trade Agreement (NAFTA), after Trump previously threatened to rip up the deal.
The central bank on Wednesday raised its 2017 growth forecast to between 1.5 percent and 2.5 percent after a stronger-than-expected first quarter, when uncertainty about Trump's policies hung over the economy. (Reporting by Michael O'Boyle; Editing by Bernadette Baum and Steve Orlofsky)