The slow-moving Rhodesia settlement conference heated up today as Britain and the Patriotic Front clashed over white rights, while the badly divided black-white Zimbabwe-Rhodesian delegation sat silent and suffered another public relations defeat.

After a weekend of sharp differences on the future role of whites between Prime Minister Abel Muzorewa and his white predecessor, Ian Smith, the Zimbabwe-Rhodesian delegation sought to minimize public embarrassment by shifting to separate negotiations with the British by both its internal factions.

The British foreign minister, Lord Carrington, seeking to settle the 14-year-old Rhodesia problem as chairman of the conference, agreed to start two-way talks Tuesday. The move may allow the Salisbury delegation to work out its differences with the British over protection for the 230,000-strong white minority without the Patriotic Front scoring propaganda victories like today's.

"The Patriotic Front ran circles around the bishop," a British source said. The British did not fare too well themselves, as the Patriotic Front accused London of trying to "saddle" an independent Zimbabwe "with the sickness of racism."

The argument arose over the issue of special white representation in Paraliament. Britain has already called for elimination of the veto power in Parliament the whites now have, leading to the split in the Zimbabwe-Rhodesian delegation. Carrington, however, wants to reserve an unspecified number of seats for whites under a new constitution.

As British officials privately seethed, Patriotic Front Spokesman Eddison Zvobgo said at a press conference that "if the British really feel strongly about the need for racial representation. . . they should lead the way" and provide for minority representation for Asians and blacks in Britain.

Both Patriotic Front leaders, Joshua Nkomo and Robert Mugabe, said earlier in the negotiations that it was "anathema to write racial privileges into the constitution."

Carrington defended the British stand saying that it is "unrealistic" to expect the whites to give up their veto power as demanded by the British "without provisions which will encourage them to forget the past and face the future as equal citizens of Zimbabwe."

The U.S.-educated Zvobgo said that the best safeguard for any groups, "whites, Moslems, Christians, tall or short people, blue or green-eyed people is that there should be no mention of these differences in the constitution."

Zimbabwe-Rhodesian Foreign Minister David Mukome, speaking immediately afterward, was defensive in response to repeated questions by reporters about his government's stand on white representation.

He said his government had a unified position on the issue, but he refused to say what it was. Asked why his delegation remained silent today, he merely said: "When you attend a conference, you can listen or talk or do both. Today we did a lot of listening."

His difficulties arose from Smith's remarks yesterday that the whites' current ability to use a veto to block constitutional changes for 10 years was "absolutely vital."

The previous day Muzorewa had hinted that he might be willing to eliminate the blocking power, saying such safeguards under black rule were "really not that important." Smith responded by saying, "I really cannot believe that anybody would say such a thing."

It is difficult to determine how inflexible Smith's stance is. Since declaring illegal independence in 1965, Smith has repeatedly adopted a hardline stance and succeeded in outmaneuvering the British. Now, however, he is minister without portfolio. Although he is the key white figure here, other whites in the delegation do not support him.

"There is nothing to prevent anybody from doing some posturing," Mukome said, thus hinting that Smith is trying to get guarantees from the British of recognition and lifting of sanctions in return for the concession.

British sources said, however, that no such deal is possible and that Carryington twice told Smith over the weekend that Britain would not accept the veto mechanism. If Smith persists in his opposition, the conference could break down. With the whites seen as the wreckers, that would virtually guarantee continuation of the seven-year-old war in which more than 100 people a day are being killed.