What is more, Trump made a number of praising remarks about Russia leader Vladimir Putin, but insisted he has no links to the Kremlin.
Some American media and supporters of Hillary Clinton openly labelled Trump as a pro-Russian candidate.
After Trump won the election he confirmed he wants a "good relationship" with Moscow.
During a phone conversation with the newly-elected president, President Putin wished him well in the implementation of his electoral program.
Moreover, Trump and Putin reportedly shared their views on combatting international terrorism and extremism, and on settling the crisis in Syria.
Trump’s adviser and former CIA director James Woolsey said in a recent interview with RT that there is a chance for normalization between Moscow and Washington.
"There are opportunities for former adversaries such as the US and Russia to work together on some things," Woolsey said.
He is "one of few people in Trump’s entourage who support resumption of contacts with the Russian government," according to Sergei Rogov, research director at the Institute for American and Canadian Studies of the Russian Academy of Sciences.
"Flynn’s appointment indicates that probably Trump wants to launch serious dialogue with Moscow. The topic and the terms of such a dialogue are unclear. But that is a fact," Rogov told RIA Novosti.
The first contacts between Donald Trump and the Chinese government revealed that a thaw between Washington and Beijing could be expected.
During phone talks, Trump and Chinese President Xi Jinping shared their interest in developing ties between the two world’s largest economies.
"During the call, the leaders established a clear sense of mutual respect for one another, and President-elect Trump stated that he believes the two leaders will have one of the strongest relationships for both countries moving forward," a statement from Trump's presidential transition office said.
During his campaign, Trump made a number of criticizing remarks towards China, including threatening to impose a 45 percent tariff on Chinese products and to label Beijing as a currency manipulator.
At the same time, Washington has sponsored Syrian rebel groups fighting the Syrian government for a long time. Washington’s official stance on the Syrian crisis contradicts with Trump’s statement.
In turn, Assad expressed hope that the Syrian government would welcome Washington’s efforts if Trump intends to fight terrorism.
"So, we cannot tell anything about what he’s [Trump] going to do, but if, let’s say if he is going to fight the terrorists, of course we are going to be ally, natural ally in that regard with the Russian, with the Iranian, with many other countries who wanted to defeat the terrorists," Assad told Portuguese television broadcaster RTP last week.
French President Francois Hollande was not very enthusiastic about Trump’s victory. According to him, this victory marked the beginning of a period of uncertainty in the United States.
"The people of the United States voted for Donald Trump. I congratulate him because this is natural in relations of presidents of two democratic countries … These elections open up a period of uncertainty," Hollande said in a statement.
Previously, he said that Trump’s victory would create difficulties in relations between Washington and Paris.
Hollande has repeatedly criticized the policy of Barack Obama’s administration.
According to Hollande, Obama’s rejection to launch airstrikes on Syria in 2013 resulted in the rise of Daesh.
At the same time, French Foreign Minister Jean-Marc Ayrault underscored Paris’ commitment to cooperation with Washington.
According to the minister, France expects that the US will clarify its position on a number of issues, including the Syrian crisis, the Iranian nuclear programme and the Paris climate deal.
The US and Israel are expected to strengthen cooperation during Trump’s presidency.
In turn, Trump invited the Israeli prime minister to pay a visit to the United States.
Netanyahu expressed hope that Israel would be able to continue the policy of "quiet diplomacy" launched under Obama’s administration.
"We will work together to advance security, stability and peace in our region," Netanyahu said in a statement.
"The bond between the US and Israel is based on shared values, shared interests and a shared future. I am sure that President-elect Trump and I will continue to strengthen the special alliance between Israel and the US and we will bring them to new heights," he added.
Earlier, Donald Trump pledged to move the US Embassy from Tel-Aviv to Jerusalem and provide unconditional support to Israel.
Traditionally warm relations between Washington and London are expected to stay the same under Trump.
After the election in the US, British Prime Minister Theresa May said the United Kingdom will remain a close ally to the US, including in the economy, security and defense.
"Britain and the United States have an enduring and special relationship based on the values of freedom, democracy and enterprise. We are, and will remain, strong and close partners on trade, security and defense," May said in a statement.
British Foreign Minister Boris Johnson echoed May’s words and wrote on Twitter he was looking forward to start working with the new US administration.
"I believe passionately in the importance of the UK-US relationship and am confident we can take it forward together," Johnson wrote.
Earlier, it was reported that the British government was considering inviting Donald Trump on an official visit next summer.
"Partnership with the United States is and remains the cornerstone of the German foreign policy. Through [this partnership] we can deal with main challenges of our time: striving for economic and social prosperity, outlooks for climate policy, fighting against terrorism, poverty, hunger and diseases, commitment to peace and freedom – in Germany, Europe and the world," Merkel said.
She also said that Germany needs to cooperate with US intelligence services in order to counter terrorist threats.
He also suggested that expanding of Iranian foreign relations after the removal of sanctions is irreversible.
At the same time, Trump said he would restructure the final agreement on Iranian deal signed under Obama’s administration.
In an interview with RT, James Woolsey said the new US presidential administration will embrace a more hardline approach towards Tehran than it was during Obama’s presidency.
One of Trump’s promises during his campaign was cancellation of the restored diplomatic ties with Cuba.
Cuban President Raul Castro congratulated Trump. However, on the day when the results of the US election were revealed, Havana announced a five-day long military exercise to prepare "to counter a range of enemy action."
After his victory, Trump also confirmed his plan to build a wall at the US-Mexican border to curb the migrant influx.
"Yes," Trump said in an interview with CBS, answering a question on whether he still wants a wall on the Mexican border.
"For certain areas I would, but certain areas, a wall is more appropriate. I’m very good at this, it’s called construction," he added.
Moreover, the Mexican economy was indirectly hit by Trump’s victory in the election due to a sharp drop in the national currency’s exchange rate. In the first hours after the election results were revealed, the Mexican peso devalued by over than 10 percent.