U.S. interest rates being kept too low for too long could cause financial instability in future and stronger market expectations for a rate rise are "probably good," St. Louis Federal Reserve President James Bullard said on Monday.

A relatively tight labor market in the United States may also exert upward pressure on inflation, raising the case for higher interest rates, Bullard added.

His comments come as financial markets have increased expectations for a U.S. interest rate hike in June or July and a range of policymakers are now stating that a rise is firmly on the table for the next policy meeting in June.

"I do worry that keeping rates too low for too long could feed into future financial instability even if it doesn't look like we're in that situation today," Bullard, a voting member of the Fed's policy-setting committee, told reporters.

Market assessment for a Fed rate rise had been close to zero, and the idea it has come off zero is "probably good," he said. "It does depend on the data and it's certainly not 100 percent, but it's not zero either. Some probability in between is the right thing to think at this point."

Bullard said the U.S. labor market was performing well and global headwinds that had partly prevented the Federal Reserve from raising rates again may have waned.

The Federal Open Market Committee has laid out a data-dependent "slow normalization" of rates, he said, thereby the nominal policy rate would gradually rise over the next several years provided the economy evolves as expected.

"Labor markets are relatively tight. This may put upward pressure on inflation going forward," he said. "This is an important factor supporting the FOMC view on the expected path of the policy rate."

Expectations for a June rate hike rose last week following minutes from the central bank's April policy meeting released on May 18 that showed Fed officials felt the U.S. economy could be ready for another interest rate increase.

A possible British exit from the European Union in a vote next month will not affect the Fed's upcoming decision on rates, Bullard said.

"Even if it's a vote to exit the EU, the next day nothing happens, because you have two years of negotiation during which new trade arrangements have to be set up," he said. "I also see the probability of an exit vote has fallen somewhat lately."

Some policymakers at the April meeting had said they were concerned financial markets could be roiled by a Brexit or by China's exchange rate policies.

In deciding whether to raise rates, the Fed looks for improvement in the economy and jobs, and evidence inflation is moving toward its 2 percent target.

The Fed last month kept its target overnight interest rate in a range of 0.25 percent to 0.50 percent. It raised interest rates in December after keeping them near zero for nearly a decade to help the economy recover from a steep recession.