Official results from Thursday's legislative election showed a higher-than-expected turnout of 42 percent, with the party that has ruled Algeria since independence 50 years ago winning comfortably and Islamists losing ground.
But Algeria's main Islamist group in the polls -- the Green Algeria alliance -- charged the polls to elect a new national assembly were fraudulent.
Clinton nonetheless said Saturday "these elections -- and the high number of women elected -- are a welcome step in Algeria's progress toward democratic reform," in a statement issued by her spokeswoman Victoria Nuland.
"The United States looks forward to working together with the newly elected National Popular Assembly and to continuing to strengthen our ties with the government and the people of Algeria," she added.
The Organisation of Islamic Cooperation also praised the "successful and democratic elections... held in an organised, transparent and peaceful manner" and recorded no irregularities.
However, European observers on the ground gave the Algerian polls a less enthusiastic report card. "We take note of a first step in the reform process which will need to be backed, after a constitutional review, by a deepening of democracy," said Ignacio Salafranca, the head of the European Union observation team.
He was delivering his 150-strong team's preliminary assessment following President Abdelaziz Bouteflika's regime's unprecedented decision to allow 500 foreign observers to monitor the polls.
Salafranca listed a number of shortcomings in the electoral process, in which 21.7 million Algerians were eligible to elect a new national assembly, but stopped short of challenging its overall credibility.
He deplored the fact that foreign observers were denied access to a nationwide electoral roll, a move he said "was not consistent with pledges of transparency."
But Salafranca reiterated his satisfaction at the generally calm atmosphere in which polling unfolded, a feeling echoed by other teams among the 500 observers who were deployed across Africa's largest country for the polls.
Algeria provides a fifth of Europe's gas, has currency reserves of more than 180 billion euros ($233 billion) and was recently asked by the International Monetary Fund to help boost its lending capacity to struggling economies.
After a campaign marked by deep voter disaffection, many Algerians however argue that the interior ministry's results were manipulated and far removed from reality. One opposition party said its own observations suggested turnout was less than half the 42 percent announced by the interior ministry.
Algeria's main Islamist group in the polls -- the Green Algeria alliance -- said the polls were fraudulent and warned that it would decide on what measures to take in a week.
The alliance's leader Bouguerra Soltani, from the Algerian branch of the Muslim Brotherhood, a party that had hoped to emulate Islamist electoral gains in the region, said the vote "wasted a golden opportunity to achieve the Algerian Spring by the ballot box."
He said the kind of Arab Spring of protests which last year unseated leaders elsewhere in the region "is only delayed" in Algeria.
The Algerian National Front, which won nine seats, announced Saturday it would challenge the results before the constitutional court over what party leader Moussa Touati called "blatant fraud". Protests that left five dead and 800 wounded broke out in January 2011 in Algeria, days after the Arab Spring's founding uprising erupted in neighbouring Tunisia.
But Bouteflika's regime, backed by the powerful military, snuffed out the movement by initiating a reform package and dishing out pay rises.
Bouteflika's National Liberation Front, which has been in power since independence from France in 1962, garnered 220 of the 462 seats up for grabs. The National Rally for Democracy, a party close to the military and loyal to the regime, mustered 68 seats, while all seven Islamist parties only managed a combined 59.