Some officials also fear Biden would attempt to salvage relations with Iran and revive the 2015 nuclear deal.
"We don't want Obama's policies to return to our country once again," said lawmaker Dhafer al-Ani, deputy head of parliament's foreign relations committee.
Mohammad Mohyi, spokesman for Kataeb Hezbollah, a hardline pro-Iran faction in Iraq, said it was time to move on.
"Trump's era was a very negative one, a period of demolition. We hope the new administration will resolve this, by ending the crisis and withdrawing its troops," he told AFP.
Mohammed also slammed Trump for committing the “greatest crime” in ordering the killing of Iranian commander Qasem Soleimani and top Iraqi commander Abu Mahdi al-Muhandis.
Several news outlets have called the race for Biden, but President Donald Trump, citing voter fraud, refuses to concede. Newsmax TV has yet to project a winner.
Nasr al-Shammary, spokesman for the Iran-aligned Harakat al-Nujaba, expressed hope at the thought of a Biden presidency.
"Perhaps choosing someone who relies on a policy of coordination could pave the way for cooperation among countries,” he said.
Khamis al-Khanjar, an influential Sunni leader who aligned with Iran in the 2018 elections, agreed.
"Biden's win is a new opportunity with the world, to turn a new page towards stability and dialogue," he said.
Iraqi President Barham Salih and Prime Minister Mustafa al-Kadhimi also congratulated Biden soon after the announcement of his victory.