NAIROBI, Kenya — Somalia’s transitional government plunged into deeper turmoil on Tuesday when the country’s president defied Parliament by appointing a new prime minister and the Kenyan government reacted by threatening sanctions.

Abdullahi Yusuf Ahmed, a former warlord who is steadily losing credibility among diplomats and foreign officials, had tried to unseat the prime minister earlier this week. The Parliament overwhelmingly rebuffed him. So on Tuesday, Mr. Yusuf announced that he had unilaterally selected another prime minister, who would be in charge of forming a new government, which Mr. Yusuf would swear in himself.

“I congratulate you,” Mr. Yusuf told a group of politicians who are supporting him and had hastily gathered at his palace in the central Somalia town of Baidoa.

Meanwhile, across town, the current prime minister, Nur Hassan Hussein, was holding a meeting with other Somali officials who claim that they are the country’s rightful leaders.

The situation now leaves Somalia with a huge crack down the middle of its beleaguered government, insurgents in control of much of the country, rising prospects of famine — and two prime ministers.

Somalia’s transitional government has never been unified, powerful, popular or effective. But the United Nations and foreign countries have supported it, with millions of dollars, because it has been seen as the least bad alternative in a war-torn country that has limped along without a functioning central government for nearly 18 years.

Several Somalis said on Tuesday that the political situation looked hopeless, but that they were not surprised.

“Disagreement seems to be part of our culture,” said Abdulkadir Hussein, a shopkeeper in Mogadishu. “Our people like conflict, rather than peace and negotiations.”

A further problem is that the Islamist insurgents who recently seized control of much of the country are also sharply divided. Many analysts predict that if the transitional government collapses — which could be soon — the Islamists will fight it out among themselves.

American officials are trying to avert this and have been pressing the United Nations to send in a peacekeeping force. But with conflicts in Congo and Sudan needing more troops, and Somalia being lawless, chaotic and incredibly violent, there are few volunteers.

One last ditch hope was a peace agreement signed by the prime minister’s team and a group of moderate Islamist opposition leaders. But Mr. Yusuf has dismissed the agreement as a “clan treaty” and called the Islamists “terrorists.”

By early afternoon on Tuesday, the Kenyan government issued a statement saying that “the action by President Yusuf further exacerbates the problem in Somalia” and that “the incessant political wrangles and competition” among Somalia’s leaders “is totally distractive” and “unhelpful to the region.”

Kenyan officials have said that if Mr. Yusuf continues to obstruct peace, he will be banned from Kenya and his assets in the country will be frozen. Mr. Yusuf is in his 70s and has been hobbled by chronic health problems since a liver transplant more than 10 years ago. He has come to Kenya many times for emergency medical treatment.