The comment in July was made by spokesman Yigal Palmor after Brazil criticised Israel's military campaign in Gaza as excessive and recalled its envoy in Tel Aviv.
In a phone call yesterday, Rivlin assured Brazil President Dilma Rousseff that Palmor's comments "do not correspond to the sentiments of the population" of Israel, Rousseff's office said in a statement.
Rousseff had criticised Palmor's remarks, saying "Words, including the spokesman's, sometimes create a very bad climate. In this case, we have to be very careful."
Israel and Hamas yesterday started a new 72-hour ceasefire, as negotiators in Egypt worked to seek a permanent end to hostilities.
Rousseff "expressed hope for the continuation of the ceasefire and the current negotiations," the statement said.
More than a month of bloody fighting in and around Gaza has killed at least 1,940 Palestinians and 67 people on the Israeli side, most of them soldiers.