Mr Corbyn said the result was a "new beginning" for the country.
Andrés Manuel López Obrador's success in the Mexican presidential election Sunday could pose profound implications for renegotiating the North American Free Trade Agreement (NAFTA).
Trump tweeted that he looked "very much forward to working with" Obrador.
He wants Trump to help pay for economic development in Mexico so Mexicans don't leave to work in the United States. Lopez Obrador has taken hits at Trump, and analysts have warned his win could ratchet up tensions between the United States and Mexico.
Do these communications mark an end to the tensions that have come between the countries since Trump's presidency? "Given the lame-duck government in Mexico and the fact that any revised NAFTA would have to be considered in 2019 by the U.S. Congress elected in November, it would not surprise me if negotiations continue at a slow pace". "It is thanks to us young people who are supporting him that he was able to get more votes than he did in past elections".
President TrumpDonald John TrumpPruitt put ally in charge of EPA office overseeing key records requests: report Scotland wind farm opposed by Trump generates first power Trump: Supreme Court pick will be a "home run" MORE has stirred fear about the numbers of Mexicans in the U.S. All the candidates are lambasting President Donald Trump's policies against migrants and Mexico. Trump has a political agenda and support base committed to a "big, lovely wall".
Surveys conducted by Consulta Mitofsky and Televisa forecast gubernatorial wins for allies of the Morena party in Chiapas, Morelos, Tabasco and Veracruz, and for head of government in Mexico City. For some, one is an economic elite of the far right, while the other is a representative of the nefarious Latin American new left.
This conciliatory tone and talk about "reaching an understanding" with the United States after the election is not what many of his voters want to see.
Alexandria Ocasio-Cortez Puts Yorktown Heights on the Map
In a two-part defense, Ocasio-Cortez shot back at Cardillo and told him to "Try Google". But Ocasio-Cortez said the label of democratic socialism did not represent her fully.
The United States, which works closely with Mexican law enforcement in its fight against drug cartels, was tired of a softening of Mexico's security policies.
If this means raising wages and creating jobs in Mexico, then this would benefit both countries.
He said Mexico's "very strong" immigration laws could be used to help keep illegal immigrants away from the US border.
Although AMLO holds a firm stance on immigration policies, he said he wants a healthy diplomacy with the U.S.
It is hard to see AMLO continuing his predecessors' security policies and anti-immigration efforts on Mexico's southern border.
It is a major shift in Mexican politics: the PRI and PAN have governed for almost a century, and Lopez Obrador will be the country's first leftist president in recent history.
And what to make of Trump's propensity for erratic behavior in matters involving Mexico? He published a book called "Oye, Trump" ("Listen Up, Trump") and he has condemned Trump's plans to build a border wall.
A majority of Mexicans seem to have exhausted of being "America's backyard". Both Republican and Democratic opposition is mounting to President Trump's potential nominee.
"The revolution of consciences has triumphed", the victor told tens of thousands of jubilant supporters who had gathered on Mexico City's central Zocalo Square.
- Trump mulls steep tariff on EU autos
- England, injured coach want no more surprises against Panama
- Foolishness killed those that died in Lagos tanker explosion - Eyewitness
- Former N.J. reporter describes 'war zone' at newsroom shooting
- Prince Harry and Meghan Markle spend Princess Diana's birthday at polo
- Melania Trump's 'I Really Don't Care' Jacket Sparks Controversy on Border Visit
- Amazon's Pharmacy Deal Threatens Retail Drugstores
- Global shares rise, oil prices jump on OPEC news
- Russian Federation beat Spain in World Cup's first penalty shootout to progress
- England vs Colombia biggest game for a decade Gareth Southgate