Karoubi asked all Iranians to take part in the election and to protect the democratic process by choosing their preferred candidate, but said: "I will vote for Rouhani".
The coalition between the two conservative nominees will benefit the country's economy in a post-election era, if Raeisi manages to assume power through the election.
Mohammed Baqer Qalibaf, the mayor of the Iranian capital of Tehran, announced he would be dropping out of the presidential election on Monday and throwing his support behind Raisi.
During a blistering presidential debate, the third and final before elections take place on May 19, Rouhani clashed with hardline candidate Ebrahim Raisi, a former high-ranking judge in Iran's Sharia-governed judicial system, during a debate over minority rights.
With Qalibaf out and Ahmadinejad rejected as a candidate by the clerical council that oversees Iran's election, Raisi now becomes the hard-liners' best hope to unseat Rouhani. The main battleground between the two factions is the selection of a successor for the Supreme Leader, in which the "reformers" have no chance given that their most prominent candidate, Hashemi Rafsanjani, a founder of the regime and former president, had a mysterious heart attack just few months ago. Mansoura Arfanian, an activist in the campaign of the conservative Ebrahim Raisi, told KUNA that the campaign has intensified publicity to lure more young citizens of diverse intellectual tendencies.
Raisi is a former prosecutor and current custodian of Astan Quds Razavi, the foundation managing the affairs of Imam Reza's shrine, which has an annual revenue of $210 billion.
Rouhani's allies say his rivals oppose deeper change and exposure to worldwide competition in part because of the economic interests of the Guards, which gained control of swathes of Iran's industry during its years of isolation. "I think that the new French President who was previously the minister of economy will continue this path for expansion of constructive relations with Iran".
Five candidates, including President Hassan Rouhani, are in the fray.
Iranian double Oscar-winning film director Asghar Farhadi has endorsed Hassan Rouhani for president, bolstering his campaign before Friday's vote.
He struck a deal with world powers in 2015 that lifted most worldwide sanctions on Iran, reconnecting it with the global financial system and opening new avenues for foreign investment, in return for curbs to Iran's disputed nuclear programme.
"A two-way race between Rouhani and Raisi will polarize society and mobilize the electorate", said Ali Vaez, senior Iran analyst at the International Crisis Group.
In the ongoing presidential campaign, Rouhani said he would focus on tackling unemployment and stimulate production.