Urging Iraqi Prime Minister Haider al-Abadi to begin talks on the issues dividing them a day, Barzani said in a televised address that the world should respect the will of Kurdish people.
Kurdistan Regional Government (KRG) leader Masoud Barzani said late Tuesday that the 'yes' vote had won with nearly 92% in the independence referendum held on Monday.
"I call on Mr Haider al-Abadi and the others (Iraqi political officials) not to close the door to dialogue because it is dialogue that will solve problems," he said.
"We assure the international community of our willingness to engage in dialogue with Baghdad," he said.
Regional authorities in Iraq's autonomous Kurdish north put the turnout at over 70 percent, but many voters reported irregularities, including cases of individuals voting multiple times and without proper registration. Official results are expected Wednesday.
Officials reported that turnout for the referendum was 72 percent, with 3.3 million of the 4.58 million registered voters taking part.
Participation was only 50 percent in Sulaimaniyah province, the home base of political forces opposed to Barzani.
His opponents have accused Barzani of seeking to empower himself through the vote, and said he should have accepted a U.N.-backed plan to postpone the referendum in favur of negotiations with Baghdad.
The KRG's decision to hold the referendum has troubled its neighbors, including Turkey and Iran, as well as the U.S., and EU, who said it will only distract from the ongoing fight against Daesh and further destabilize the region.
Statements from U.N. Secretary-General Antonio Guterres also expressed regret that the vote was held and said issues between Iraq's federal government and Kurdish region should be resolved through dialogue.
Iraqi prime minister al-Abadi had declared before the vote he would take "necessary measures" to protect Iraqi unity, and he was due to meet parliament members on Wednesday.
Fearing the vote could be used to redraw Iraq's borders, taking a sizeable part of the country's oil wealth with it, al-Abadi has called the referendum an act of "sedition" that "escalated the ethnic and sectarian tension" across the country.
The vote is non-binding and will not lead automatically to independence, but is seen by the Kurds as a major step towards a long-cherished dream of statehood.