In particular, they hoped President Gurbanguly Berdymukhammedov would break away from years of repression and pardon political prisoners jailed under his predecessor.
However, the much-awaited amnesty has not happened and nothing indicates that it will. Although engaged in economic and social changes, Berdymukhammedov has given confusing signals as to whether he is a political reformist.
The Turkmen Supreme Court sentenced former parliament speaker Ovezgeldy Ataev -- who should have constitutionally succeeded Niyazov as interim leader -- to five years in jail on charges of driving his stepson's bride to suicide.
Observers have contrasting opinions of Berdymukhammedov.
To some, especially among the exiled opposition, the new Turkmen leader is a product of the political system inherited from late President Saparmurat Niyazov and no real democratic reforms should be expected from him.
But to others, Berdymukhammedov could enter history as the Turkmen equal of Nikita Khrushchev, the architect of Soviet de-Stalinization, also known as the "thaw."
"Will the 20th session of the Halk Maslahaty turn into a kind of 20th congress of the CPSU [Communist Party of the Soviet Union]?" read the rhetorical headlines of an analytical paper posted on the ferghana.ru website before Turkmenistan's supreme legislative body convened in the southeastern city of Mary.
The author argued that despite the similarity in ordinal numbers, it would be illusory to expect any radical political reforms from that assembly, if only because the freshly elected president was too busy consolidating his power.
Berdymukhammedov has started delivering on the pledges for social and economic reforms he made in the run-up to the February 11 polls, focusing his attention on Turkmenistan's agriculture, education, and health systems -- which were left in shambles by Niyazov's destructive policies.
No Real Political Changes
But there have not yet been any political reforms. With the exception of a few cosmetic adjustments, Niyazov's personality cult remains largely untouched.
If Turkmenistan's media have become more informative, they still operate under strict government control and censorship.
Berdymukhammedov -- who rose to power through conspiratorial methods and an election that offered no real choice to voters -- remains impervious to the notion of political pluralism and keeps Niyazov's exiled political opponents at bay.
The New York-based nongovernmental organization Human Rights Watch says in an April 12 report that "the only sign of possible political reform" the new leader has given so far is a promise to make the Internet more accessible to Turkmen.
Yet, even this announcement remains largely symbolic.
The two government-sponsored Internet cafes that have opened in Ashgabat are charging their clients up to 60,000 manats ($11.50) per hour, an exorbitant fee by local standards.
Restricted Internet Access
The presence of soldiers at the doors -- at least in the days following the February opening -- and the obligation to show one's passport prior to using a computer are likely to further dissuade potential customers.
Reports that authorities are considering hiring Chinese experts to help keep electronic communications under strict control are yet another indication that Turkmen may not have free access to the Internet for a long time.
In the field of human rights, the situation is equally disheartening.
In January, a Turkmen court freed Andrei Zatoka, a Russian environmentalist who had been arrested a few days before Niyazov's death on charges that were fabricated. This judicial decision eventually proved a red herring.
First, because the move was clearly meant to accommodate the Kremlin, which had demanded Zatoka's release. Second, because the defendant left the courtroom with a three year-suspended prison sentence.
In the days that immediately followed his election, Berdymukhammedov ordered the creation of a state commission to review individual complaints against law enforcement agencies.
Liberalizing Move Or Infighting?
The initiative -- which Berdymukhammedov described as "a step toward developing democratic principles in the functioning of state and society" -- led many, both inside and outside the country, to believe it heralded the end of Turkmenistan's years of repression.
Less than two months after the commission was set up, Berdymukhammedov sacked Interior Minister Akmammed Rakhmanov, blaming him for the corruption, drug trafficking, racketeering, and black marketing he said had become a trademark of Turkmen police.
The Turkmen president told Rakhmanov's successor, Khojamyrat Annagurbanov, to "efficiently protect individual rights and freedoms," the official TDH news agency reported on April 9.
It's unclear whether Rakhmanov's removal should be interpreted as a harbinger of liberalization or the result of infighting among the top political leadership.
Between the February presidential election and the Halk Maslahaty session, there was widespread speculation that Berdymukhammedov would inaugurate his term with a broad political amnesty.
Those hopes were prompted by news that authorities had started dismantling the infamous Ovadan-Tepe prison colony, where Niyazov had kept his political opponents and most former government officials who had fallen into disfavor with him.
Former Turkmen President Niyazov (file photo)
Information received by RFE/RL's Turkmen Service indicates Ovadan-Tepe inmates have been either put under house arrest or transferred to other detention facilities. Among them is former Prosecutor-General Gurbanbibi Atajanova who, according to the Vienna-based Turkmen Initiative for Human Rights (TI), is now in a women's prison colony in the northwestern city of Dashhowuz.
RFE/RL's Turkmen Service reports former Deputy Prime Minister Yolly Gurbanmuradov -- who was sentenced to 25 years in jail in 2005 on charges of misappropriating state funds -- is believed to be under house arrest. Yet his whereabouts are unknown and the TI says his wife remains in Dashhowuz prison.
The Oazis website reported on March 28 that Geldy Kyarizov -- the former head of Turkmenistan's state horse farms (Turkmenatlar) who is serving a six-year prison sentence -- remains in jail despite being "in a state of complete exhaustion."
Independent reports posted on various opposition websites say Berdymukhammedov has turned down requests for amnesty filed by relatives of more than 50 political prisoners. The reasons for his refusal are unclear.
Meanwhile, the specter of the Niyazov-era repression continues to hang over the country.
Despite the extradition denial by the Varna City court earlier this month, Ashgabat is still seeking the return of Annadurdy Khajiev, an opposition leader and former Central Bank deputy chairman who has been living in Bulgaria since 2001.
In February, the Turkmen Supreme Court sentenced former parliament speaker Ovezgeldy Ataev five years in jail on charges of driving his stepson's bride to suicide.
Ataev, who should have constitutionally succeeded Niyazov as interim leader, was arrested on December 22 and was kept incommunicado until his closed trial.
The TI reports that Ataev's wife also received a jail sentence and was sent to Dashhowuz. The group says this shows that the practice -- widespread under Niyazov -- of collectively sentencing members of the same family continues.
The talks that Louise Arbour, the UN high commissioner for human rights, will have with Berdymukhammedov in Ashgabat on May 3-5 will be a benchmark to measure his democratic credentials.
Perhaps more important than the talks themselves will be how the visit will be covered by Turkmen state media.