The head of state said he expected the new cabinet led by Kosor to continue pursuing an unequivocal and resolute pro-European policy.
At a ceremony televised by the national broadcasting company, Kosor said she hoped that the new government would be appointed on Monday and announced a revision of the state budget as her first move as the country's premier.
"Ms. Kosor has presented evidence showing that in the present make-up of the Sabor (national parliament) she has the backing of the required majority," Mesic said.
He went on to say that it was now up to the Croatian Democratic Union (HDZ) and parties which have decided or will decide to be its coalition partner to make next moves.
He also urged for the continuation of reforms, anti-corruption struggle and full cooperation with the Hague-based International Criminal Tribunal for the former Yugoslavia, as well as for commitment to the full respect of human and ethnic minorities' rights and to enabling all refugees to return to their prewar homes.
Mesic said that every Croatian government must be committed to Croatia's anti-Fascist pillars.
Thanking Mesic for his confidence in her as the PM-Designate, Kosor said that all what he said would be in the programme of her cabinet.
She voiced hope that Croatia's European Union accession negotiations, blocked by Slovenia due to a border dispute, would resume by the end of this year.
Kosor announced the revision of the coalition agreement as regards the current situation.
The outgoing Prime Minister and HDZ head Sanader on Wednesday withdrew from his government and party duties as well as from active politics, but would not clearly explain the reasons for this decision at an extraordinary news conference.
Sanader only said he had made the decision after deep consideration, and recalled that he had been in politics 20 years, and at the helm of the HDZ for 10 years.
On that occasion Sanader said that Kosor would succeed him at the helm of the government and as their party's chief.
In the meantime the HDZ ensured the support of a majority of members of parliament for Kosor's appointment as the new PM and Mesic held consultations with all parliamentary parties, as envisaged by the law on the government.
The parliament is expected to approve Kosor's cabinet on Monday.