The United States has regularly accused Iran of undermining security in Iraq by funding, equipping and training Iraqi militants, a charge Tehran dismisses saying U.S. forces are the destabilising influence and should leave.
Some Iraqi officials have also talked of "interference" by Iran, which like Iraq is majority Shi'ite, while others have urged Iran and the United States not to fight a proxy war in Iraq.
"Perhaps the best way of thinking regarding the issue of constructive engagement at this delicate moment is for all neighbours to carefully respect the sovereignty, the unity of the country and work for its stability," Staffan de Mistura told a news conference in Tehran.
"And the key word probably is sovereignty. That will be the filter through which, I presume, the Iraqis will judge what is constructive and non-constructive," the U.N. envoy added.
De Mistura, who held talks with top Iranian officials in Tehran, said that the call for "constructive engagement" was a message he had already taken to other neighbours such as Jordan, Turkey and Kuwait.
"We all know that there is a very strong involvement of Iran in Iraq and a strong influence," he said, describing Iran as a "very, very important neighbour of Iraq."
He said neighbours could constructively engage by continuing regional meetings on security, energy and refugees.
Asked if Iran's role was constructive now, he said: "I don't have enough elements to be able to define how the role is because I can only judge on what I am seeing and what we want to see, which is a further involvement in the field we just mentioned."
De Mistura said Iran had helped Iraq by, for example, investing in Iraqi electricity supplies.
The U.N. envoy earlier met President Mahmoud Ahmadinejad, Foreign Minister Manouchehr Mottaki, Parliament Speaker Ali Larijani and other senior officials. (Reporting by Edmund Blair; editing by Sami Aboudi)
