A U.S. Federal Reserve rate hike in June or July wasn't set in stone, but labor data suggested it was time to pull the trigger, St. Louis Fed President James Bullard told CNBC.

"There's no reason to prejudge June," Bullard said, adding that the Federal Open Markets Committee would look at the data and decide then.

Muddying the waters on the timing of the move, Bullard noted that there was no reason the Fed must hold a press conference in conjunction with a rate hike. A press conference is scheduled to follow the June 14-15 meeting, but one is not scheduled after the July 26-27 meeting.

"We can wait until we get to the meeting, see what the latest data says, and try to make a good decision there. I think on the issue of press conferences, we have made many moves over the years without press conferences," he said.

"So I think you can make a move without press conferences in this circumstance. I think for that first move, you know the one we did in December, there you probably wanted to have a press conference around that because that was our first move. Whether you have to do that for every single move, I think it is questionable."

For Bullard, labor data was sending a clear signal.

"If you just took your signal from [labor market data], we'd definitely move," he said, noting labor was "at or beyond" full employment, with the number of unemployed persons per job opening lower than during the previous expansion.

"I think we are at or beyond full employment in the U.S., so in the labour market side, that's probably the strongest argument for going ahead and making a move," Bullard said.

But he added that other data were not as strong, with tracking estimates for gross domestic product (GDP) growth this quarter at around 1.6 percent, below the 2 percent trend growth expected.

The Fed kept its target overnight interest rate in a range of 0.25 percent to 0.50 percent at its April meeting, but the meeting's minutes specifically mentioned June as a time when it could hike rates. The Fed hiked rates in December for the first time in nearly a decade.

One thing that, unexpectedly, may not factor in to the Fed's decision-making: The U.S. presidential election.

"The Fed has moved during political cycles in the past," Bullard said, noting that the central bank started a tightening cycle during the 2004 presidential election year.

"Monetary policy is largely independent of the political process. And one of the things I think is you can't win an election by talking about whether the Fed should move right or move left," he said.

Additionally, markets may be fixated on whether the U.K. would vote to leave the European Union (EU), an event dubbed the "Brexit," and if that would throw a speed bump onto the Fed's hiking path, but Bullard said he did not consider it "quite the global financial market event that some are saying," although he noted his view could be "an outlier."