He warned of a "rough ride" hours after President Donald Trump was sworn in.
Enrique Pena Nieto cautioned in his Twitter message that the sovereignty, national interest and protection of Mexicans would be paramount, but he said he hoped ties between the two countries would strengthen.
"They have sanctions on Russian Federation - let's see if we can make some good deals with Russian Federation".
"For one thing, I think nuclear weapons should be way down and reduced very substantially, that's part of it".
However, on December 22 Trump tweeted that the USA must "greatly strengthen and expand its nuclear capability until the world comes to its senses regarding nukes".
The dossier reportedly contained a freaky story of Trump allegedly hiring prostitutes to "perform a "golden showers" show in front of him" on a hotel bed in the Ritz Carlton presidential suite in the Russian capital, where Barack Obama and his wife had previously stayed.
He said he would seek "respectful" dialogue with Mr Trump, who angered many Mexicans on the campaign trail by deriding them as rapists and murderers, and vowing to build a massive wall along the U.S. border to keep them out.
German Foreign Minister Frank-Walter Steinmeier said Trump's view that North Atlantic Treaty Organisation was obsolete and his criticism that European allied members aren't paying their fair share had "caused astonishment".
Mr Trump's praise for Mr Putin has raised expectations that he could move to normalise ties, although Mr Trump hasn't articulated a clear policy and some of his cabinet nominees have made hawkish statements on Russian Federation.
The interview was conducted by Michael Gove, a Conservative Party member and prominent Brexit campaigner who is known to be close to Rupert Murdoch, owner of Fox News.
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Lavrov said Moscow is inviting representatives of the incoming USA administration to attend talks Monday on Syria in Kazakhstan, discussions brokered by Russia, Turkey and Iran.
Konstantin Kosachev, head of the upper house of parliament's worldwide affairs committee, was cited by the RIA Novosti news agency as saying getting the sanctions annulled was not a goal in itself and not worth making security concessions.
U.S. President Barack Obama said Wednesday that having a constructive relationship with Russian Federation is in the interest of the U.S. and the world. It alleged that Trump was groomed and supported by Russian intelligence and that the Kremlin was in possession of compromising material on the president-elect. A stark warning on Putin's plans for Europe, NATO, and us.
The store, located across the street from the USA embassy, hailed Inauguration Day with posters showing a fist-pumping Trump clad in red power tie under a banner featuring the army's iconic red-star logo.
Mr. Lavrov said that Moscow did not interpret recent remarks by Mr. Trump as an offer to scrap sanctions imposed by the United States over Russia's actions in Ukraine and elsewhere in exchange for a nuclear arms reduction deal. In an interview with The Wall Street Journal last week, Mr. Trump suggested he would be open to lifting sanctions on Russian Federation.
The contact, as Obama imposed sanctions, raised questions about whether Trump's team discussed - or even helped shape - Russia's response.
Russian President Vladimir Putin is accusing the outgoing U.S. administration of trying to undermine President-elect Donald Trump by spreading fake allegations. Trump said that if Putin likes him, "That's called an asset, not a liability".
The statement reflected the Kremlin's boiling anger at President Barack Obama's administration, which declined to comment on Putin's accusation.
Meanwhile he has said on Putin: "I think it would be great to get along with him".