In a special gesture, Trump and the first lady Melania came out on the South Portico of the White House to receive Modi.
Trump and his wife warmly welcomed Modi and they were seen exchanging pleasantries and having a brief interaction before going inside the White House.
As the two leaders sat for the meeting, Modi expressed gratitude to Trump and the first lady for the warm welcome extended to him.
The prime minister said Trump has been paying attention to India's growth march and economic progress.
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Among the issues on the table were counter-terrorism cooperation, defence partnership, global cooperation, trade and energy.
The tone for the first summit meeting was set by the US State Department which declared Syed Salahuddin, chief of Kashmiri militant group Hizbul Mujahideen, as a 'global terrorist', just a few hours earlier.
Ahead of the meeting, Modi said the logic of the Indo-US strategic ties is "incontrovertible" and the two countries have an overriding interest in securing the world from terrorism, radical ideologies and non-traditional security threats.
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