Iran and Turkey, a North Atlantic Treaty Organisation member, overwhelmingly opposed the non-binding referendum vote, over fears the move could ignite independence movements by Kurdish populations in their own countries.
Iranian President Hassan Rouhani and Erdogan vowed to work closely together to prevent the disintegration of Iraq and Syria and to oppose the Iraqi Kurds' drive for independence.
The Iranian defense minister said those behind Iraq's partition must know that they are certainly playing in the hands of the U.S. and the Israeli regime "because regional countries need peace, security and stability and any move contrary to regional people's demands is doomed to failure".
Tensions have been running high between Iraqi government and the Kurdish region after the region held a controversial referendum on independence of Kurdistan and disputed areas, including Kirkuk.
"We welcome expansion of political, cultural, economic and scientific relations with Ireland", he said during a meeting with Chairman of the Senate of the Republic of Ireland Denis O'Donovan in Tehran. Both have threatened sanctions on the Kurdish Regional Government (KRG) in Iraq. "Our determination in this regard is clear".
"As far as we are concerned, Iraq is one single country", he said.
Recep Tayyip Erdogan is expected to arrive in Tehran on Wednesday.
Turkey also has sizeable Kurdish population -14 million, out of a total population of about 81 million - that resides in the southeast of the country and bordering Iraq and Iran's Kurdish territories.
"There is no country other than Israel that recognizes it".
A day later, Prime Minister Benjamin rejected the claims and took a shot at Erdogan for blaming Mossad meddling for every tricky situation Turkey faces.
Turkish armed forces chief of staff General Hulusi Akar also came to visit the Iranian capital on Sunday.
The Kurds are the region's fourth largest ethnic group, spread across Iran, Turkey, Syria and Iraq, all of which oppose any moves towards sovereignty.
Baghdad already has imposed sanctions on Kurdish banks and halted foreign currency transfers to the region, and a flight ban has halted all global flights from servicing the Iraqi Kurdish territory's airports.
The military drills, contributed by some forces of the Iraqi Army, is conducted near the Parviz Khan border post in western Iran.
Calling the referendum "illegitimate", Erdogan said that "a development of this sort will isolate the Kurdish regional government".
"It was the people who determined their future in the referendum", he said.
Erdogan, in a translation on Iranian state television of his comments, warned of "stronger" measures to follow and said the autonomous Kurdish region in northern Iraq would remain "isolated".