Cabinet minister Steve Kent confirmed his candidacy on Twitter on Thursday, promising to find solutions to health care issues and ways of diversifying the economy.
Health Minister Paul Davis and former cabinet minister John Ottenheimer have also announced their candidacies.
Nominations close Monday and a leadership convention is scheduled for the weekend of Sept. 12.
The party has been in power since 2003 and began the search for a new leader in January when Premier Kathy Dunderdale quit politics amid complaints about her leadership style.
The process of replacing her was thrown into disarray last month when Corner Brook businessman Frank Coleman announced he was pulling out of the race, citing an undisclosed challenge facing an immediate family member.
Coleman became the sole leadership candidate in April when fisheries magnate Bill Barry quit the race, but Coleman's decision meant the Tories had to restart the contest from scratch.
Kent is the minister of municipal and intergovernmental affairs and represents the St. John's-area riding of Mount Pearl North in the legislature.