He said on live television the proposed ministers of education, Mohammad Ali Najafi, of science, research and technology, Jafar Mili-Monfared -- both considered close to reformists -- and Massoud Sontanifar, at sports and youth, were rejected during Thursday voting session.
Among the key nominations approved by the conservative-dominated Majlis were Mohammad Javad Zari as foreign minister and Bijan Zanganeh for the oil portfolio.
Voting was on a candidate-by-candidate basis and not on the 18-member cabinet as a whole. Rouhani now has three months to fill the three posts left vacant.
Zanganeh, who is highly respected in the energy industry and on the international scene, already served as oil minister between 1997 and 2005 under reformist president Mohammad Khatami.
But he faced heavy criticism during the four days of parliamentary debate on newly-elected Rouhani's nominations, for both his ties to reformists and over alleged corruption in oil contracts.
As for the new foreign minister, Zarif, who holds a US doctorate in international law, served as the Islamic Republic's ambassador to the United Nations between 2002 and 2007.
He also played a leading role in nuclear negotiations between Iran and world powers in 2003-2005 at a time when Rouhani led his country's delegation.
Rouhani has said the priority of his all-male team of technocrats will be to tackle Iran's economic crisis and its nuclear program in a bid to lift several rounds of punishing Western sanctions.
In another key appointment, Ali Akbar Salehi, the foreign minister in the government of Rouhani's predecessor Mahmoud Ahmadinejad, was named to head Iran's Atomic Energy Organization.
Salehi, who holds a doctorate in nuclear science from the Massachusetts Institute of Technology, already headed the organization between 2009 and 2010 before taking up the post of foreign minister.
In an address to parliament at the start of the debate on Monday, Rouhani laid stress on Iran's ailing economy and condemned the Western methods to apply pressure.
International sanctions have crippled the once lucrative oil sector, cut its access to global banking and contributed to soaring inflation.
He added that "in the field of diplomacy, the government was going to try to tackle this international challenge while defending the nation's will" to hold on to its nuclear rights.
At his first press conference after taking office on August 4, Rouhani had urged "serious" talks with the international community without delay to allay concerns about Iran's nuclear program.
But he said he would not surrender Iran's "rights" to enrich uranium for civilian energy purposes.
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