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"I believe their (Trump-Russia) relationship would result in solving most of the problems", Rajapaksa told reporters marking his 71st birthday in Colombo on Friday.
Talking about an impact of Trump's presidency on Sri Lanka, Rajapaksa said, "We hope US interference in our country would decrease (under Trump)."
Rajapaksa's 10-year rule saw a thorny relationship with President Barack Obama's administration.
The Democratic Party government led as many as three UN Human Rights Council resolutions on the Rajapaksa government's human rights accountability.
Rajapaksa blamed his 2015 election defeat on certain international governments.