(Adds comments on interest rates, peso and U.S.-Mexico relationship)
By Alexandra Alper
WASHINGTON, April 20 (Reuters) - Mexico's central bank governor Agustin Carstens signaled on Thursday that the bank's cycle of monetary tightening might not be over, saying that there were "still some issues that need to be taken care of."
Speaking at an event in Washington, Banco de Mexico chief Carstens said the bank had mostly fulfilled its role of preventing price increases from becoming generalized, and that inflation expectations had largely stabilized.
But he added that markets still needed some convincing that inflation was well-anchored.
"We are happy with what we have achieved," Carstens said when asked if the bank's tightening cycle was over, "but there are still some issues that need to be taken care of."
"I would say the gap between where we want to be and where we are has been decreasing," Cartens said.
Banco de Mexico had increased the benchmark interest rate to a nearly 8-year high with a string of 50-basis point hikes before introducing a smaller increase, 25 points, in its last board meeting.
Carstens said the bank had moved quickly to adjust interest rates above U.S. interest rates, which he said was key to helping stabilize the exchange rate.
Earlier this month, Carstens said that Banco de Mexico may stop reacting to decisions by the U.S. Federal Reserve, depending on the evolution of inflation expectations.
Carstens said that the peso is still undervalued and does not fully reflect the fundamentals of Mexico. The U.S.-Mexico relationship has evolved favorably and should continue to improve, he added.
The peso hit record lows following Donald Trump's victory in the November U.S. presidential election but has recovered in recent weeks to about 18.8 per dollar as recent comments from U.S. officials suggested a softer approach to Mexico.
In an interview late on Wednesday, Finance Minister Jose Antonio Meade told Reuters that the peso is "quite competitive" and could strengthen further despite likely bouts of volatility.
Mexico sends about 80 percent of its exports to the United States, and Trump's threats to ditch the North American Free Trade Agreement (NAFTA) that underpins commerce in the region sparked fears of a sharp downturn in the economy.
Lately, though, those concerns have eased somewhat.
Carstens said any renegotiation of NAFTA could result in a win-win for Mexico and the United States. He added that inflation had moved out of the central bank's 2 to 4 percent target range because of changes to gasoline prices and the nominal exchange rate. (Reporting by Alexandra Alper; Editing by Bernard Orr)