At a press conference in Tehran, Rouhani, considered a moderate in Iran's political system which also encompasses factions of hardline conservatives and reformists, praised the electorate for backing his allies at the ballot box in the February 26 polls.
The 67-year-old president has faced opposition in parliament, including on his landmark nuclear deal with world powers, and his officials have also been shouted down when addressing lawmakers.
"I am very pleased that mostly the moderate candidates made it to the parliament," Rouhani said.
"This means that the people of Iran have chosen moderation and opened that path. This is a message from the people to all officials" of the Islamic republic, he added, saying it paved the way for much brighter prospects than in recent years.
The elections were a de-facto referendum on Rouhani's administration as the electorate could have delivered a stinging rebuke only one month after the nuclear deal was finally implemented and sanctions lifted in January.
But instead many of those lawmakers who had hit out at the agreement, which reined in Iran's atomic ambitions in exchange for sanctions relief, lost their seats.
Although no single political grouping won a majority in the 290-seat parliament, the recent conservative dominance of the chamber was markedly curbed.
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Conservatives won 103 seats and a pro-Rouhani coalition of moderates and reformists, dubbed the "List of Hope", won 95, with other seats going to Independents and minorities and 69 constituencies requiring a second ballot in April.
However even many of those conservatives are considered moderate in outlook, meaning the pragmatic Rouhani is likely to be able to win support for future legislation he proposes, a shift that he noted.
"Many bills were not passed," he said, referring to his government's problems with parliament since he took office in August 2013. "There were many impeachment motions," he added.
But the election results mean Iran's people will have "a parliament that can cooperate with government, rather than one that confronts it", he said.
"I am very confident that cooperation will rise this time, compared to the last parliament."
Having concluded the nuclear deal, Rouhani is expected to push for sweeping economic reform to allow the country to cash in on foreign business interest since the nuclear deal. Last week he said the country's auto sector should be privatised.
After their recent tie-up for the election, reformists may also pressure Rouhani to push for social and cultural changes he promised when standing for president but has not yet progressed.
The president will also have to wait a while to test the ground. With the second round of voting for MPs not taking place until April, the new parliament will not be sworn in until late May.