The White House moved yesterday to end two weeks of hostilities with Senate Republicans as chief of staff Donald T. Regan brought a two-foot-long peace pipe to Majority Leader Robert J. Dole (R-Kan.) and as President Reagan offered to make phone calls to help resolve the Senate's budget dispute with the House.

But, responding to Dole's suggestion Sunday that Reagan "step into the breach" to achieve a budget compromise, White House officials appeared to be trying to keep some distance between the president and the budget fracas.

"I don't think Reagan is going to ride a white horse to Capitol Hill on this one, but he'll be there and his presence will be forceful," said White House spokesman Larry Speakes. It is a "matter for Congress" to resolve, Speakes said. "The White House has been with them every step of the way, and it's up to them."

Congressional negotiations over a fiscal 1986 budget broke down last week, jeopardizing about $250 billion in deficit reductions for the next three years, after the White House agreed with House Democrats and Republicans to abandon a Senate proposal to freeze Social Security benefits for a year.

This angered Senate Republicans, who felt they had been left out on a shaky limb on the sensitive Social Security issue. Their anger intensified after Regan called the budget dispute "ridiculous."

Dole, clearly miffed at Regan, suggested at one point that, while the Senate Republicans needed and wanted the president's help, they could do without Regan.

Yesterday was Dole's 62nd birthday, and Regan arrived for a meeting on farm legislation with a package that turned out to contain a ceremonial peace pipe, trimmed with leather and beads, from the Pipestone National Monument in Minnesota.

"I just wanted Senate Republicans to know I'm at peace with them," Regan said.

"Is there anything ticking?" quipped Dole.

Reagan called Dole to convey birthday greetings and, Dole said, indicated "he wanted to be helpful" in breaking the budget stalemate.

Senate and House Republican leaders are planning to meet today at the White House to discuss the budget. Senate leaders have been discussing options in private but reportedly have yet to make the basic policy decision on how far to go in compromising with the House.

Before breaking off the talks last Wednesday, Senate negotiators rejected as insufficient a House offer to make an additional $24 billion in cuts in domestic programs over three years.

Defending that offer yesterday, House Budget Committee Chairman William H. Gray III (D-Pa.) said the basic problem was not the offer but "disarray" among the Republicans and added, "We can't solve that." Said Gray: "The problem is they've got internal conflicts they have to resolve."

As expected, Gray and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) took a dim view of Dole's suggestion Sunday for an every-other-year inflation adjustment for both Social Security benefits and income taxes. Both are currently adjusted annually for inflation. In offering the idea, Dole said he didn't think it would go far.

Meanwhile, House and Senate conferees began negotiations on a $13 billion-plus supplemental appropriation for the rest of the current fiscal year, which ends Sept. 30. Progress was reported on water projects, including a cost-sharing plan demanded by the Senate.

Other issues include whether to let the Central Intelligence Agency handle aid to antigovernment rebels in Nicaragua, which the Senate wants and the House opposes, and economic aid to Jordan, proposed by the Senate but not the House.