Jaafari met with Iranian counterpart Mohammad Javad Zarif and was scheduled to meet President Hassan Rouhani later, the official IRNA news agency said.
Zarif and Jaafari discussed "regional and international issues", the report said, and they were to hold a joint press conference around 0830 GMT.
Shiite-majority Iraq's government has close ties with Tehran.
The ISNA news agency reported that Jaafari was making efforts to "advance dialogue and have a diplomatic role in preventing efforts to create discord", so that the region could "pass its current challenge".
The visit came after the crisis between Saudi Arabia and Iran widened on Tuesday when Kuwait recalled its ambassador to Tehran and Bahrain severed air links with the Islamic republic.
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Joining Riyadh and its Sunni Arab allies in taking diplomatic action, Kuwait said it was withdrawing its envoy following an arson attack at the Saudi embassy in Tehran.
The violence came after Saudi Arabia's execution of Sheikh Nimr al-Nimr, a prominent Shiite cleric accused of fomenting sedition in the Sunni-ruled kingdom.
Iran condemned the killing again on Tuesday, with Rouhani accusing Riyadh of seeking to "cover its crime" by severing ties.
The United States and other Western powers have called for calm amid fears the dispute could raise sectarian tensions across the Middle East and derail efforts to resolve bloody conflicts in Syria and Yemen.
There were protests in Iran, Iraq, Lebanon, Bahrain and Pakistan after Nimr's execution.
Iraq's top Shiite authority, Grand Ayatollah Ali al-Sistani, said the execution was an unjustified act of aggression.
Saudi Arabia only recently re-opened its embassy in Baghdad and Nimr's execution sparked calls among protesters for it to be closed and the ambassador expelled.