The S&P/TSX composite index ended the day down three points at 14,753.05.
South of the border, markets posted a strong advance as the U.S. Federal Reserve began a two-day meeting where its is expected to maintain the status quo on rates that have been at historically low levels since the Great Recession.
However, the gains in New York were not enough to reverse the losses of the previous two sessions when a breakdown in talks on Greece's sovereign debt crisis brought out the bears.
The Dow Jones industrial average closed up 113.31 points at 17,904.48 after the widely watched index suffered triple-digit losses on Friday and again on Monday.
The Nasdaq rose 25.58 points to 5,055.55, while the S&P 500 added 11.86 points to 2,096.29.
Gareth Watson, vice-president of investment management and research at Richardson GMP Ltd., said the stabilizing of the price of oil around US$60 has had a mediating effect on the Canadian market.
Developments in Greece and the Federal Reserve meeting are less important in the short term to the health of the Canadian economy than changes in oil and other commodity prices, he said.
"To be blunt, there's not a heck of a lot of stuff out there influencing the Canadian market," Watson said.
He added that Canada and world markets have become more insulated from a potential Greek exit from the euro as that country's debt problems have dragged on over the years.
"Of course, there will be some type of financial disruption if that is the eventual course of action," he said. "We have to deal with this day-to-day volatility talking about it, but in the long run I don't see Greece taking down the global market to any real extent."
The loonie ended the day up 0.03 of a U.S. cent at 81.22 cents.
It's unlikely that the Canadian dollar will return to parity in the coming months, Watson said, given the expectation that the United States will raise rates closer to the end of the year.
"Overall, you can't get too bullish on the Canadian dollar when it appears the U.S. will be raising rates long before we will," Watson said.
In commodities, the July oil contract was up 45 cents at US$59.97 a barrel. Watson said the supply glut that has cut prices by more than $40 since July 2014 shows no sign of abating.
August gold lost $4.90 to close at US$1,180.90 an ounce.