With no obvious heir to Saparmurat Niyazov, the late president, who died of heart failure on Thursday, commentators said would-be successors were maneuvering behind the scenes.
They also said Niyazov's sudden death could lead to a contest between Russia and the West over the former Soviet republic's enormous natural gas and petroleum reserves.
Vladimir Putin, the Russian president, said in a condolence message that "strengthening our partnership is in the true interests of the peoples of Russia and Turkmenistan."
George Bush, the US president, said the US hopes "to expand our relations with Turkmenistan."
Rich in resources
Turkmenistan's natural gas deposits are second only to Russia's among the former Soviet states. All its gas now flows through Russian pipelines, and critics accuse the Kremlin of using its control of energy supplies to exert political pressure on its neighbours.
Niyazov signed an agreement this year to build a gas pipeline to China, with its growing energy needs.
For years, the US has sought transit routes for Central Asia's oil and gas that would bypass Russia. Washington has lobbied for a pipeline from Turkmenistan across the Caspian Sea to the west, skirting Russia's southern border.
The struggle for power in Ashkhabad, the capital, will be closely watched.
"This will determine who takes control of the gas wealth of Turkmenistan," the Russian newspaper Komsomolskaya Pravda said. "Moscow or Washington."
Opposition come back
Khudaiberdy Orazov, Turkmenistan's former central bank chief living in exile in Sweden, told The Associated Press that he and two other opposition leaders planned to return home to compete in the presidential election.
Another expatriate, Avdy Kuliyev, former foreign minister, told Russia's RIA-Novosti news agency that he planned to return from Norway. "We must hurry to Turkmenistan because time is on the side of the Niyazovite group," he said.
Azhdar Kurtov, an analyst with the Moscow-based Institute for Strategic Research, predicted Turkmenistan's security agencies would tightly control the election.
"The Turkmen people won't face any democratic choice in the elections," he said. "A single candidate with no alternatives will be put forward for whom everybody will have to vote."
Niyazov won Turkmenistan's last presidential elections in 1992 with a reported 95.5 per cent of the vote. He was named president for life in 1999.
Arkady Dubnov, a Central Asia expert with the Russian newspaper Vremya Novostei, said a fierce internal power struggle was under way. Years of repression and one-man rule, he said, have left the country without alternative political leaders.
The interim president, Dubnov said, is a temporary figure: the real potential heir is the chief of Niyazov's presidential guard, Akmurad Redzhepov.
Analysts said powerful security officials stood behind Berdymukhamedov, a deputy prime minister, who is likely only an interim leader. His rise to power was swift and surprising.
Under the constitution, Ovezgeldy Atayev, a parliament speaker, was next in line for the presidency. But shortly after Niyazov's death was announced, Atayev was charged with abuse of power and human rights violations.
Berdymukhamedov signed an order dismissing Atayev for "committing a deed incompatible with the high position entrusted him."
Turkmenistan's prosecutor general accused Atayev in a statement of harassing and humiliating his own daughter-in-law and driving her to attempt suicide.
Berdymukhamedov said the People's Council, a 2,000-member legislature chosen by Niyazov, will meet Tuesday to pick the candidates and set a date for presidential elections. But a decree the acting president signed suggested any elections may not be competitive.
"National presidential elections will be held on a democratic basis that has been laid by the great leader," the decree said, referring to Niyazov.
A country in mourning
Ashkhabad appeared calm on the second day of mourning. Turkmen newspapers, all state-controlled, devoted all their coverage to Niyazov's death. They carried front-page photographs of the late president and - in a Soviet tradition - reaction and condolences from citizens and staff of various enterprises.
"Our hearts are overflowing with sorrow, feeling the pain of a loss, an irreplaceable loss" said the somber headlines in the official Neutral Turkmenistan newspaper.
All restaurants, cafes and liquor shops were closed throughout the country. Weddings were ordered to be postponed until December 30, the end of the national mourning period. Niyazov's funeral is scheduled for Sunday.