The suggestions of alternative sites raised the possibility of complications to get talks under way as expected on April 13 between Iran and envoys from the five permanent UN Security Council members and Germany. It also could bring accusations of stall tactics by Iran's leaders.
Iran's foreign minister, Ali Akbar Salehi, said İstanbul was Iran's first choice as a venue. It has now been publicly cited by the US and others as the site of the talks. But Salehi appeared to leave open the possibility, however small, that the negotiations could shift to another location.
"Holding talks in Baghdad, and also China, as venue has been out there," Salehi told reporters after a Cabinet meeting in Tehran. "This is a course that both sides need to agree on ... İstanbul was our initial proposal as the venue for the talks. The Europeans initially rejected but then agreed. At the same time, we had other countries in mind."
In Baghdad, Iraqi Foreign Minister Hoshyar Zebari confirmed that an Iranian delegation proposed Baghdad for the talks during a visit to Iraq on Tuesday.
"The proposal came from them. We received a delegation from Iran ... Today we are inviting G5 plus one ambassadors to hand over a letter about the proposal," Zebari told Reuters.
A Western diplomat in Baghdad confirmed envoys had been called to Iraq's foreign ministry for a meeting on Wednesday.
There was no immediate reaction from Turkey or the six powers - the United States, Britain, France, Russia, China and Germany - to the proposal to hold talks in Iraq.
Salehi noted that the content of the talks is "more important than the venue and timing."
"I think the future talks, compared to the past, will hopefully be better and forward steps will be taken," he said.
Talks broke down in January 2011 over Iran's refusal to halt uranium enrichment in exchange for reactor-ready fuel from abroad. The West and others fear Iran could use its ability to make nuclear fuel as the foundation for an eventual atomic weapons program. Iran insists it only seeks nuclear power for energy and medical research.
US Secretary of State Hillary Clinton announced the April 13-14 negotiations would take place in İstanbul, the first such meeting since January 2011 when the sides did not even manage to agree on an agenda.
Iran's relationship with Turkey has been strained recently by Turkish pressures on Syrian President Bashar Assad, a vital ally for Tehran. Clinton and other leaders met this week in İstanbul to seek ways to aid the Syrian opposition in their year-old rebellion against Assad's regime.
Turkey has demanded Assad halt a year-long crackdown on opponents in Syria and step down. Last month, Turkey also announced it would reduce the amount of oil it buys from Iran by 10 percent, ceding to US pressure over Iran sanctions.
A senior Iranian figure recently spoke out against Turkey hosting the talks. "Given the fact that our friends in Turkey have failed to fulfill some of our agreements, the talks... had better be held in another friendly country," former presidential candidate Mohsen Rezaie, who is now secretary of the Expediency Council -- an influential body that advises Iran's Supreme Leader Ayatollah Ali Khamenei, who directs nuclear policy -- said. Rezaie said that Baghdad, Damascus or Beirut would be a more suitable venue.
"Offering İstanbul as the venue for the upcoming talks ... might give this wrong impression to the opposite side that Iran has grown weak and is in weak conditions," he added.
Iran has close ties with the government of Iraqi Prime Minister Nouri al-Maliki. China remains a key trade partner and has strongly opposed Western sanctions targeting Iran's critical oil exports.
Pulling back from years of war, Iraq last month hosted the Arab League summit for the first time in two decades, as part of Baghdad's push to return to the diplomatic stage in a region split along sectarian lines over the Syrian uprising and Western sanctions on Iran.