Yes . . . more or less.
According to the introduction to the section on the Council of Trent in (Norman P. Tanner, SJ, ed. Decrees of the Ecumenical Councils, 2 vols., 1990, II:657-8), Pope Paul III in 1537 attempted to summon a council to the cities of Mantua and then Vicenza to respond to the Protestant Reformation. This effort ended in failure. Later in 1542 he summoned a council to the city of Trent. This summons also failed because a war that broke out between Francis I, king of France and the emperor Charles V. With the Peace of Crépy in 1544 Paul III was able to announce the council in Trent in the bull Laetare Jerusalem (19 Nov 1544). The council was convened 13 Dec 1545.
1st Period - 1545-48: sessions 1-10 - Paul III
2nd Period - 1551-52: sessions 11-16 - Julius III
3rd Period - 1562-63: sessions 17-25 - Pius IV
It should be noted that the introductions to each Council in Tanner is taken from that provided in the latest edition of Conciliorum Oecumenicorum Decreta, ed. G. Alberigo, et al., 3rd edition, Bologna, Istituto per le Scienze Religiose, 1973. This is the text Tanner’s translaters used.