Before taking the oath of office on Tuesday, national assembly leader Mr Pereira said Guinea-Bissau was "facing a very delicate situation".
He called on MPs "to assume their responsibility toward the nation".
Lawmakers in the capital Bissau also observed a moment of silence for President Vieira and for the army chief-of-staff Gen Tagme Na Waie.
Life in the city began to return to normal with some businesses re-opening, although shoppers briefly fled two market places in panic after rumours spread of fresh shooting, according to Reuters news agency.
Guinea Bissau swears in new leader
The United Nations Security Council "condemns in the strongest terms the assassinations," the 15-member body said in a statement.
"The Security Council reaffirms its commitment to support the efforts of the government and people of Guinea-Bissau to consolidate democratic institutions, peace and stability in that country".
The statement also said the council "opposes any attempt to change the government through unconstitutional means".
Diplomats representing West African and Portuguese-speaking nations have also said they hope the constitution will be honoured.
Nigerian President Umaru Yar'Adua, who heads the 15-member regional bloc Ecowas, has sent a delegation to the country.
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