The order builds on sweeping restrictions issued last week by Trump that TikTok and WeChat end all operations in the US, his latest explosive moves aimed at countering China's rising global power.
"I heard it today that she doesn't meet the requirements," Trump said at a White House news conference on Thursday, referring to an August 12 opinion piece in Newsweek.
"A neighbour isn't just someone who shares our geography but those who share our hearts. Where the relationship is respected, it becomes warmer," he said.
In annual celebrations scaled down due to the COVID-19 pandemic, Modi identified health and economic self-reliance as the key priorities for his government.