TORONTO -- North American equity markets were narrowly mixed Tuesday amid investor caution over the outcome of Thursday's referendum when Britons will decided whether to remain in the European Union.

The Toronto Stock Exchange's S&P/TSX composite index closed down 2.82 points at 14,012.32 as traders took a breather after solid gains Monday in the wake of new polls showing British voters leading towards remaining in the EU.

"The big move kind of was yesterday. What we're seeing today is a little bit of people sitting on their hands," said Michael Greenberg, portfolio manager at Franklin Templeton Solutions.

"I don't think there are too many investors who have enough real conviction one way or the other whether it's an exit or a remain to really put big bets on. So I think we're seeing a bit of a wait-and-see here until Thursday or probably more like Friday morning when we get the results."

Major New York indexes were all positive, although modestly so, after having swung between slight gains and losses earlier in the day.

The Dow Jones industrials finished up 24.86 points at 17,829.73, while the S&P 500 added 5.65 points to 2,088.90 and the Nasdaq edged up 6.55 points to 4,843.76.

The late-day gains in New York followed what investors took to be positive remarks from Federal Reserve chairwoman Janet Yellen, who told the Senate that the U.S. central bank needs to proceed cautiously on raising interest rates in the face of a number of economic uncertainties.

Among other things, Yellen said the Fed will watch carefully to see if the recent slowdown in job growth is temporary or a sign of a bigger problem.

"It was really pretty consistent with what she said last week at the FOMC (Federal Open Market Committee) meeting," Greenberg said.

"But I'd say, at the margin a little bit more dovish, a little less confidence ... There were some phrases in there that would lead you to believe that she was maybe a little less optimistic" on the pace of the U.S. economic recovery.

Meanwhile, the oil-sensitive Canadian dollar declined 0.01 of a U.S. cent to 78.06 cents US as the August contract for North American benchmark crude settled down 11 cents at US$49.85 a barrel after two days of strong gains.

Greenberg said he expects oil to bounce around between $45 and $55 a barrel over the rest of the year barring any major geopolitical event.

"Between $45 and $55 is kind of the break even levels for a lot of the shale oil producers," he said. "So if you get much above that range they start producing more and that should bring prices down. If prices get much below that they kind of cut production and cut supply and should bring prices up."

Elsewhere in commodities, the July contract for natural gas finished up two cents at US$2.77 per mmBtu, while August gold was down $19.60 at US$1,272.50 a troy ounce and July copper added just over two cents to US$2.12 a pound.