Prime Minister Yasuhiro Nakasone has promised Canadian Prime Minister Brian Mulroney that "he will seek to settle" the issue of broadening the Group of Five into a Group of Seven before the end of the economic summit here on Tuesday, a senior Canadian official told reporters today.

The Group of Five, which now comprises the United States, Japan, West Germany, France and Britain, would be expanded to include the other two summit nations, Canada and Italy.

Under the leadership of Treasury Secretary James A. Baker III, the G-5's finance ministers and central bankers have assumed a major role in international economic policy. For example, last Sept. 22, in New York, it undertook a coordinated intervention that drove down the exchange rate of the dollar.

A lower dollar rate makes American products more competitive in foreign markets, helping to reduce the U.S. trade deficit, which the nations agreed had been unsettling the international economic system.

There was no assurance, despite Nakasone's commitment to press the issue, that the enlargement of the group would actually be accomplished before the end of the summit, given the drain on the leaders' time occasioned by the growing agenda of other issues.

But there also was no doubt that Canada and Italy would continue to press for the change. Canadian officials assert that as one of the world's major economic powers, Canada has the right to be involved in decisions affecting its exchange and interest rates. Italy makes similar arguments.

"There are major transformations taking place in the world economy," the Canadian official said following the Nakasone-Mulroney meeting, "and Canada is interested, indeed concerned to play a role in that."

President Reagan had also committed himself to the concept during a recent meeting with Mulroney in Washington. But resistance has come from West Germany and Britain, which say that expansion of the group could make it less effective.

The Canadians and Italians have resented their exclusion since the G-5 was formed in the 1970s, but especially since the Versailles summit in 1982 and the Williamsburg summit in 1983 directed the finance ministers of the G-5 nations to take a larger role in studying international monetary reform.