A meeting called to smooth relations between Republican National Chairman Richard Richards and New Right conservatives yesterday erupted into an angry debate over the role of independent campaign expenditures by conservative groups.

The debate, according to several participants, pitted Richards, who has been highly critical of the groups, against a who's who of the leadership of the New Right, including Terry Dolan, chairman of the National Conservative Political Action Committee, direct mail expert Richard A. Viguerie and Paul M. Weyrich, chairman of the Committee for Survival of a Free Congress.

The two-hour breakfast was officially off the record and key New Right participants refused to comment on it. "We all had an opportunity to state our respective positions," Richards said in a prepared statement. "We will attempt to formulate an agreement as to our respective positions, including how we will disagree, if at all, in the future."

Richards apparently understated the acrimony of the meeting. "There were some very strong comments made about whether money raised by political action committees should be channeled through one committee," one participant said.

Dolan reportedly was particularly adamant about defending the right of his NCPAC to undertake independent campaigns against Liberal Democrats, like Sens. Paul S. Sarbanes of Maryland and Edward M. Kennedy of Massachusetts.

"As they say in diplomatic circles, it was a frank and open discussion," another participant said. "Although there may have been some fiery words, nobody swung a punch. Everyone there understood Dick Richards is head of the Republican National Committee, not the conservative national committee. Most of us consider ourselves conservatives first, and Republicans second."

White House political adviser Lyn Nofziger initiated the meeting between Richards and more than 20 New Right leaders after the national GOP chairman last month said independent groups, like NCPAC, "create all kinds of mischief" and have the potential of damaging President Reagan.

Although his remarks sparked a public disagreement with Nofziger, Richards has refused to retreat. In a meeting with Washington Post editors and reporters Monday, the chairman said, "My quarrel is that independent expenditure groups butt in on the strategy of a campaign."

Richards conceded they may "soften" up opponents early in a campaign, but he added, "The problem is they stay too long, they say the wrong things and ultimately they may be counterproductive."

Among others at yesterday's meeting at the Capitol Hill Club were Howard J. Phillips of the Conservative Caucus, Thomas Ellis of Sen. Jesse A. Helms' North Carolina-based Congressional Club, Phyllis Schlafly of Eagle Forum, Ronald Godwin of Moral Majority, Robert C. Heckman of the Fund for a Conservative Majority and Robert Richardson of Gun Owners of America.