Observers who for the first time were allowed to monitor elections in Jordan said Friday that the vote showed a marked improvement from past polls, but there is still some way to go.

An international team fielded by the National Democratic Institute, made up of 50 observers from 29 countries, highlighted "shortcomings and irregularities," as well as certain systemic problems.

"The unequal size of districts and an electoral system that amplifies family, tribal and national cleavages limit the development of a truly national legislative body and challenge King Abdullah's stated aim of encouraging 'full parliamentary government,' " it said.

But, the institute said, the improvements seen "should give competitors and voters in this and future electoral contests more confidence that their votes are counted fairly and their choices reflected through the election system."

About 1.3 million Jordanians went to the polls in Wednesday's balloting, representing 56.6% of registered voters according to the newly instituted Independent Elections Commission.

The vote was held amid political tensions and calls for wider reform.

Opposition groups, including the Muslim Brotherhood, boycotted the election, saying the country's new electoral laws -- brought in by Jordan's ruler, King Abdullah II, after protests -- favored the monarchy.

Nimer al-Assaf, deputy secretary general of the Islamic Action Front, the political wing of the Muslim Brotherhood in Jordan, told CNN the election "was as expected -- just a mere copy of the parliament that was dissolved."

He disputed the official turnout numbers, but added, "even if they were true, still only one-third of Jordanians participated, so it's not really representative."

More than 3 million Jordanians were eligible to vote for candidates to the new 150-member House of Deputies, officials said.

King Abdullah, speaking at the World Economic Forum in Switzerland on Friday, challenged the criticisms made by the Muslim Brotherhood.

"At the beginning, the doubters out there and the opposition didn't think anyone would register to vote. We had an unprecedented registration, 70%, which is much higher than any other country in the Middle East," he said. "Again, the turnout of 56.6% (announced) yesterday was way beyond anybody's expectations."

These figures indicate the country's leaders and the people have "moved on," Abdullah said. He suggested that the Muslim Brotherhood should do the same, in order to be part of an inclusive political future.

Buying of votes

Polling was held under the watchful eye of 47,000 police officers and another 7,000 election observers.

David Martin, head of the European Union's Election Observation Mission in Jordan, praised the way balloting was handled but, like the National Democratic Institute, pointed to systemic problems.

"Technically, the elections were remarkably organized," he told CNN on Friday. "The IEC did an excellent job ensuring that those who wanted to vote could vote in secret. And the counting was proficiently professional."

He said his mission's estimate of turnout was as high as 60%, broadly in line with that of the IEC.

"Our criticism is that the elections were conducted within a weak legal framework and that the system didn't lead itself to an even outcome," he said.

There were some violent incidents, concentrated in Maan, Tafileh, and Karak, and some districts in Amman -- some within tribes, others between tribes and some concerning individuals, he said.

But while such violence is "unacceptable and not helpful to the process," the incidents seem to have been unconnected. "Although we are always concerned about violence, we are not worried this was a concerted attempt to undermine the credibility of the elections," Martin said.

However, an issue to be addressed is that of illegal campaigning outside polling centers, Martin said.

CNN reporters witnessed many people passing out fliers, pamphlets and cards promoting specific candidates outside polling stations.

Another observer group, the International Republican Institute, said its teams -- deployed at more than 175 polling stations -- saw illegal campaigning "outside the majority" it visited.

The institute said it had also heard numerous allegations of vote-buying on election day, despite improved enforcement of rules banning this in the run-up to the vote.