Al-Zebari said that while militants have been infiltrating into Iraq from Iran, Tehran does not approve of such actions.
"We are sure the Islamic Republic [Iran] does not want Al-Qaeda and Abu Mus'ab al-Zarqawi on our lands," al-Zebari said.
The Iranian foreign minister's visit came just two days after U.S. Secretary of State Condoleezza Rice paid a surprise visit to Baghdad and three weeks after the formation of a Shi'ite-dominated government.
Several Shi'ite members of the new cabinet lived for years in exile in Iran.
Kharrazi held talks with Iraqi Prime Minister Ibrahim al-Ja'fari, President Jalal Talabani, and al-Zebari. He pledged to cooperate with Baghdad on security and not interfere in Iraqi internal matters.
"We have done our best so that the borders between the two countries are under control. And for that reason, we have arrested many people who have been involved in weapons smuggling because we believe that [securing] the borders of the two countries is [securing] the Islamic Republic [of Iran]," Kharrazi said.
Iran and Iraq established full diplomatic ties last year for the first time since the end of their 1980s war that left 1 million dead.
Relations have slowly improved since the ouster of Saddam Hussein in March 2003. But U.S. officials and several former interim Iraqi officials have accused Iran of meddling in Baghdad's internal affairs, manipulating the country's political process and supporting the insurgency. Iranian officials have repeatedly denied the charges, saying Iran backs Iraq's stability and sovereignty.
Alireza Nourizadeh is a political analyst and the head of the Center for Arab-Iranian Studies in London. He says Kharazzi's trip to Baghdad is a goodwill gesture and a new start in the ties between the two countries.
"The head of the new Iraqi cabinet and a number of the ministers are considered friends of the Islamic Republic. Considering the fact that under the government of [former interim Prime Minister] Iyad Alawi, despite trips by officials from both countries, Iraqis always criticized Iranian interference, this trip is the beginning of new ties and also it will lead to fewer complaints and more Iranian cooperation with a government whose members have said from the beginning is willing to have friendly ties with Iran," Nourizadeh said.
Al-Zebari said he had no doubt that Kharrazi's visit "will open up significant new horizons for cooperation between the two countries." Iran's foreign minister also said it is in Iran's interest to support the Iraqi government by all means.
Shaul Bakhash is an expert on Iran at George Mason University near Washington. He told "The New York Times" that Kharrazi's visit shows Iraq's leaders are eager to recognize the key role that Iran -- with its 1,300-kilometer border with Iraq, trade possibilities and Shi'ite faith -- will play in Iraq's future.
After his talks in Baghdad, Kharrazi said Iran does not want to use its emerging ties with U.S.-supported Iraq as a way to settle its sharp differences with Washington.
He said: "Whatever our relations with the United States may be, we think it is our duty to assist the Iraqi people."