Ties between the two former war parties were strained when Iraq's US-appointed interim defence minister Hazim Shaalan accused the Muslim neighbour of being his country's "number one enemy".
On 26 July, Shaalan warned of invading Iran if it did not stop what he called interference in his country's internal politics.
"I've seen clear interference in Iraqi issues by Iran," the minister said in an interview with The Washington Post in Baghdad on Monday.
"Iran interferes in order to kill democracy."
Shaalan defended his statements while accompanying Allawi to Saudi Arabia.
"In a statement made in the Saudi city of Jidda, Shaalan added that his statements to The Washington Post newspaper were enough to send an Iraqi message to Iran", Aljazeera's correspondent in the city said.
While in Saudi Arabia, Allawi and the Kingdom's Foreign Minister
Saud al-Faisal bin Abd al-Aziz agreed to reopen their embassies which have been closed since Iraq's invasion of Kuwait in 1990 and the use of Saudi Arabia as a launchpad for the 1991 Gulf War.
"We have agreed to open up embassies between Saudi Arabia
and Iraq," Allawi told reporters.