BEIRUT, Lebanon (CNN) -- Saad Hariri is poised to follow in his father's footsteps and become Lebanon's next prime minister, a position he said he "will not shy away from."
Saad Hariri said he will discuss taking the position of Lebanon's prime minister with his allies.
"I will discuss it with my allies," the pro-U.S. Sunni lawmaker told CNN. "You know, I didn't win this election by myself. My allies had a big role to play in winning for the 14th of March (coalition). And I think it will only be fair and obvious that we talk, me and my allies ... and then after that, if I have to do it, I will not shy away from it."
Hariri is the head of the "March 14" coalition, which retained its control over Lebanon's government this week despite a strong challenge from a Hezbollah-dominated alliance.
Hariri said he hopes to accomplish what his father, former Prime Minister Rafik Hariri, never had a chance to do before he was killed in 2005.
"He accomplished in his assassination the sovereignty of Lebanon, the independence of Lebanon," Hariri said. "And I want to accomplish what he always dreamt of Lebanon being.
"I think he would want me to do what's good for Lebanon, do what would unite the Lebanese people, and ... concentrate on the economy and the security and stability of Lebanon."
The elder Hariri was killed in a massive bombing in February 2005 that also left 22 others dead. An ongoing United Nations investigation has found indications of Syrian involvement in the assassination of the popular statesman, but Syria has denied any role.
His death triggered massive protests that eventually led to the withdrawal of Syrian forces, ending Syria's occupation of Lebanon.
Saad Hariri said Sunday's vote "was about Lebanon" and not its precarious position between its alliances with Western countries and its Arab neighbors.
"The people who went on the 7th of June voted for Lebanon first," he said. "It's not about the West; it's not about Iran; it's not about Syria. It's about we as Lebanese, what we want from this new parliament and from this new government that's going to come."
Hariri ruled out an independent peace track with Israel, sticking by his previous assessment that Lebanon will be the last country to sign a peace deal with the Jewish state.
"We will follow after the Arab initiative," he said. "You see, the Arab initiative includes many countries for the peace process, and Lebanon will come as we see fit."
Israel fought a war against Hezbollah militants in Lebanon three years ago that is widely regarded as having empowered the Shiite militia, which claimed victory in the six-week conflict.
Some analysts had feared that a Hezbollah victory in this week's parliamentary elections would have heightened tensions in the Middle East, particularly because of the estimated 30,000 rockets pointed at Israel from southern Lebanon, all under the control of Hezbollah militants.
Hariri met Tuesday with President Carter, who is in Beirut with more than 200 international observers monitoring the election. Shortly before that meeting, Hariri said the United States will play a key role in the effort to attain peace in the Middle East.
"I think the biggest turning point in this peace process is what the United States will do," he said. "The United States has a big role to play, and if it plays it in the right way, if it plays its role like it should play it, then we will have peace in the region. They should pressure both sides to move forward -- whether the Palestinians and the Israelis, whether the Syrians and the Israelis -- and I'm sure we'll get there."
After the victory of Hariri's coalition, the next step for Lebanese lawmakers will be to elect a speaker of the parliament. Then, Lebanese President Michel Sleiman will ask someone -- presumably Hariri -- to form a government.
In Lebanon, the presidency is reserved for Maronite Christians, the speaker of parliament is always a Shia Muslim, and the prime minister is a Sunni Muslim. That system was created to balance power among Lebanon's three main religious groups.