"I ask the prime minister to propose to me within seven days from today [Friday] the format of a new credible Independent Electoral Commission which will organise fair and transparent elections," he said.
The move throws into doubt the political reconciliation process in the divided country that had former rebels serving in top ministerial posts.
Monica Mark, a journalist based in Abidjan, the Ivorian capital, told Al Jazeera the opposition had addressed a news conference at which they announced they no longer recognised Bbagbo's legitimacy.
She quoted the opposition as saying that "the action to dissove parliament and the independent electoral commission, which is supposed to be independent of the president, amounts to a coup d'etat".
"They've effectively made a very loaded statement saying Ivorians will resort to any means necessary to oppose dictatorship ... The situation is very tense at the moment," Mark said.
The dissolution followed a decision by Soro this week to suspend the process of registering voters indefinitely because of rising tensions, casting doubt on when the long delayed presidential election would take place.
Investigators said last week that they had found evidence of fraud in a voters' roll being compiled for long-delayed polls because the election panel had used a compact disc with unauthorised names.
The electoral commission refutes the allegations but has acknowledged major problems in managing voter lists.
The elections are needed to end years of instability and stalemate following a 2002-2003 war that divided the world's top cocoa grower into a rebel-held north and a government-controlled south.
They have been postponed repeatedly since 2005 but had been scheduled for the end of this month or early March.