Mexico City authorities have removed a controversial statue of the former Azeri leader from its current location.
Workers moved the four-metre tall sculpture of Heydar Aliyev in the dead of night from a park on the city's main avenue that Azerbaijan paid to have renovated.
Oil-rich Azerbaijan has threatened to cut investments in Mexico in response.
Human rights activists had objected to the statue and pointed to the repressive nature of Mr Aliyev's rule.
Mexico City officials said that "dialogue would continue with the aim of finding a permanent location for the sculpture".
They said city authorities would look after the statue in the meantime, unless the Azeri Embassy requested its return.
When the previous mayor of Mexico City, Marcelo Ebrard, unveiled the Azerbaijan-Mexico Park last year, he said it was a "testament to the will of the two peoples to grow closer".
Mr Ebrard also noted that - in 16 years - none of the 180 diplomatic missions or 45 international organisations based in Mexico City had given as much money for public spaces in the capital as Azerbaijan.
Azeri investments in Mexico amount to $4bn (£2.5bn), according to the Azeri embassy in Mexico.
A plaque accompanying the statue describes Aliyev as "a great politician and statesman".
In Azerbaijan there is a growing personality cult surrounding the former leader, who is regarded as a father of the nation, which became independent after the collapse of the Soviet Union, the BBC's Damien McGuinness reports from neighbouring Georgia.
His face can be seen on huge billboards all over the country, our correspondent adds.
Mr Aliyev's son Ilham has ruled the country since 2003 - but with presidential elections in October, and growing concerns in the West about the government's human rights record, Azerbaijan is keen to promote his father's image abroad, he says.