At a press conference in New Delhi yesterday, Indian Prime Minister Narendra Modi spoke about how he had been informed about Singapore's plans to put driverless cars on the road.

"But we all rest assured that one of India's strongest well-wishers, Prime Minister Lee, is in the driving seat for Singapore and for our bilateral relationship," he quipped to laughter.

Mr Lee Hsien Loong, standing next to him, broke into a wide grin.

That captured the tone for the day as the the two leaders met yesterday at Hyderabad House, where foreign dignitaries visiting India are usually hosted.

After working meetings, both leaders spoke at a joint press conference of the deepening ties between their countries.

Mr Lee thanked his host for his "very warm welcome and his warm words", and credited India's transformation and optimism about its prospects to Mr Modi's dynamic leadership and clear vision.

Mr Modi called Singapore a key partner on India's journey of strong economic growth and transformation.

"I deeply value your personal friendship, and your leadership in taking our bilateral relationship forward," Mr Modi said to Mr Lee, whom he called a friend of India.

The mutual desire to advance these bilateral ties was at the core of both leaders' remarks yesterday, the second day of Mr Lee's five-day working trip to India.

He was most recently in the country in 2012, while Mr Modi last visited Singapore in November last year.

Both men had exchanged messages on Twitter earlier yesterday before they met, with Mr Lee saying he was looking forward to meeting Mr Modi, and Mr Modi welcoming Mr Lee to India.

There were also sombre moments yesterday, such as when Mr Modi recalled that his first visit to Singapore as prime minister was for a "solemn occasion" last year, to pay respects to the late Mr Lee Kuan Yew, Singapore's founding Prime Minister.

Mr Modi also said he was saddened by the death in August of former president S R Nathan, who was "a close friend of India".

Mr Nathan had been conferred the Pravasi Bharatiya Samman, the highest honour India gives overseas Indians. Mr Modi said: "We will miss him."

Mr Lee also offered his condolences to the Indian government and to the families of those killed and injured during an attack last month on the Uri army base in Kashmir.

He said: "Singapore strongly condemns terrorist attacks of all forms."

Later, Mr Lee, who treated Mr Modi to supper at Komala Vilas last year, was hosted by the Indian Prime Minister to a sumptuous meal with a spread of no fewer than 14 North and South Indian dishes.

Mr Lee also received a call by Indian External Affairs Minister Sushma Swaraj, and met about 200 Singaporeans based in India at a dinner reception.