The Rhodesia settlement conference became mired today in a maze of walkout hints, delays and conflicting statements all too reminiscent of past abortive attempts to solve the intractable 14-year-old independence problem.

The British-sponsored conference slowed to a snail's pace as the morning session to discuss London's constitutional proposals was called off at the request of the Zimbabwe-Rhodesian government.The afternoon session lasted only 35 minutes as both the government and the rival Patriotic Front guerrillas asked for more time to study the plan.

White former prime minister Ian Smith, who apparently differed with Zimbabwe-Rhodesian Prime Minister Abel Muzorewa during yesterday's meeting, missed today's session on grounds of illness.

Another member of the government delegation, the Rev. Ndabaningi Sithole, also stayed away from the meeting, leading to reports of a split in the Salisbury team. He denied a split but issued a statement critical of the Muzorewa government.

Muzorewa said at a press conference that he may leave the talks after agreement is reached on a constitution, thus ignoring the view of the rival Patriotic Front guerrillas that a new constitution is only a small part of an overall settlement to end the seven-year-old war.

The day of confusion contrasted with yesterday's relatively successful negotiations in which agreement was reached on an agenda linking agreement on a constitution and transitional arrangements leading to independence.

British spokesmen cautioned, however, that such hassles are to be expected in dealing with the Rhodesia problem and that British Foreign Secretary Lord Carrington, who is chairing the conference, was not dismayed.

Muzorewa took a tough public stance in his press conference, saying, "We came here to talk about the constitution and when that is over why should we stay here in London."

His threat recalled the abortive 1976 Geneva conference where Smith said he would discuss nothing but a plan devised by former U.S. secretary of state Henry Kissinger. This time Muzorewa is saying he came to London only to discuss the constitution.

In addition, he made a stong plea for Western recognition of his embattled government, which retains strong elements of control for the 230,000 white minority among the population of 7 million.

In a reference to Britain, the United States and Europe, he said the only reason for lack of recognition and continuing sanctions was "lack of honesty, courage and integrity by those countries who should be our friends and encourage us." He cited thepossibility of greater "participation for the Russians, the East Germans and the Cubans" in the war.

He also showed annoyance at reporters' questions about divisions in his government delegation, citing apparent support given by Smith yesterday to the two-part agenda. He said he was the only person who spoke for the delegation, which is made up of four parties involved in his government.

British Prime Minister Margaret Thatcher made her first appearance, having tea with the delegates at the conference, which was called as a result of her diplomacy at the Commonwealth Conference in Lusaka, Zambia last month.