Two of the Republican Party's leading presidential aspirants and longtime rivals, Rep. Jack Kemp of New York and Senate Majority Leader Robert J. Dole of Kansas, arranged a private truce this week in their increasingly tart public feud.

After a week of bitter exchanges between them, Kemp telephoned Dole on Monday to suggest that both should cool their attacks on each other.

Dole said through an aide yesterday that "they both agreed it was a little bit early for the fireworks over 1988 to start."

Kemp and Dole, who have had a long-running disagreement over taxes and the deficit, are not expected to abandon their sharply divergent viewpoints as the 1988 campaign for a successor to President Reagan grows closer.

Dole has staked much of his political future on reducing the deficit, Kemp on passage of legislation to overhaul the federal tax code.

Their frequent jostling became more intense recently when Kemp urged White House chief of staff Donald T. Regan to abandon a one-year freeze on Social Security cost-of-living adjustments in an effort to break the deadlock in Congress over the budget. Senate Republicans had voted for the freeze at Dole's urging and at some peril to their 1986 reelection campaigns; many House Republicans opposed it.

Dole expressed indignation that the White House was giving up on the Social Security freeze. He blamed Regan and "noisy House Republicans" for the decision, saying it amounted to "surrendering to the deficit."

But the majority leader muted his criticism of Kemp in an appearance Sunday on NBC's "Meet the Press." He said, "I think I make harder choices sometimes than he does, but the quarrel is not between two members of Congress."

Seeing the program, Kemp called Monday to say he appreciated Dole's restrained approach, according to John Buckley, Kemp's press secretary.

While both Republicans will continue to disagree on many issues, Kemp wanted to dampen the "public rancor," Buckley said.

And the congressman wanted to tell Dole that "all the news stories about a feud were stories that Jack hoped were certainly not true," the aide said.

"It doesn't make sense for two leaders of their party to be involved in public contentiousness, especially when there are a great many things they can work together on, such as reducing the deficit and getting tax reform this year," he said.

Kemp's call apparently reflected a concern that continued quarreling with Dole could crimp the prospects for tax reform and enterprise zone legislation.

For similar reasons, Kemp pulled back a direct-mail fund-raising appeal that was aimed at House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) when the speaker objected to it.