Against the backdrop of tensions between Tehran and Riyadh, the official Qatar News Agency said Tamim bin Hamad Al-Thani telephoned Rouhani on the occasion of the Eid al-Adha feast, which Muslims began celebrating on Monday.
"The emir stressed that Gulf-Iran relations should be based on good neighbourly relations and mutual respect," reported QNA.
"Any Gulf-Iran disputes should be settled through negotiations and dialogue," the emir was quoted as saying.
QNA did not say specifically when the call was made.
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It comes at a time of increased tensions and a full-scale war of words between opposing regional powerhouses Iran and Saudi Arabia over the hajj pilgrimage.
Iranians were this year blocked from joining the pilgrimage to Islam's holiest sites in Saudi Arabia for the first time in almost 30 years.
In response, Tehran called on the Muslim world to "punish" the Saudi government for its handling of the pilgrimage following last year's stampede disaster during the hajj.
In addition, Saudi Arabia's most senior cleric, Grand Mufti Abdul Aziz al-Sheikh, called Iranians "not Muslims".
And Iran's supreme leader Ayatollah Ali Khamenei blasted the "incompetence" of the Saudi royal family.
The trading of insults comes on top of deep and bitter political schisms which sees the two countries support different sides in the Yemeni and Syrian conflicts.