The United States and India share a historic bond as the world's oldest and largest democracies, US President Donald Trump said on Monday as he greeted India on its 77th Republic Day celebrations.

Trump's greetings came amid continuing strain in ties between the two countries over a range of issues, including Washington's policies on trade and tariffs.

"On behalf of the people of the United States, I extend my heartfelt congratulations to the government and people of India as you celebrate your 77th Republic Day," the US president said.

"The United States and India share a historic bond as the world's oldest and largest democracies," he added.

Trump's message was put out on social media by the US embassy in New Delhi.

US Secretary of State Marco Rubio also extended greetings to India on the occasion of the Republic Day and said the two nations share a "historic bond".

"From our close cooperation on defense, energy, critical minerals, and emerging technologies to our multi-layered engagement through the Quad, the US-India relationship delivers real results for our two countries and for the Indo-Pacific region," he said.

"I look forward to working together to advance our shared objectives in the year ahead," Rubio said in a statement.

US ambassador to India Sergio Gor also greeted India after attending the Republic Day celebrations at the Kartavya Path.

"Happy Republic Day, India! Honored to attend the Republic Day Parade for the first time, a celebration of India’s Constitution and democratic spirit. Thrilled to see the US-made aircraft soaring in the Indian sky, a powerful symbol of the strength of the US-India strategic partnership," he said.

US-origin transport aircraft C-130J and Apache helicopters were among the aerial platforms that figured in the parade.

The India-US ties witnessed a major downturn after President Donald Trump slapped a whopping 50 per cent tariffs on Indian goods, including a 25 per cent punitive levy over Russian oil purchases.

Both sides have held multiple rounds of negotiations last year to firm up the proposed bilateral trade deal. However, it could not be sealed yet, largely in view of Washington's demands to open up India's farm and dairy sectors.

Apart from the tariff issue, the relations came under strain on a number of other issues that included US President Donald Trump's claim of ending the India-Pakistan conflict in May last year and Washington's new immigration policy.

Except for the headline, this story has not been edited by The Telegraph Online staff and has been published from a syndicated feed.