Contact with Chandrayaan-2 was lost moments before its Vikram module was due to touch down at the lunar south pole.
The fate of the craft is not yet known, but Mr Modi said there would be further opportunities.
India would have been the fourth nation to make a soft landing on the Moon.
"The best is yet to come in our space programme. India is with you," said Mr Modi.
The Chandrayaan-2 approached the Moon as normal until an error occurred about 2.1km (1.3 miles) from the surface, officials said.
India's Space Research Organization (Isro) said it lost contact seconds before the ship was expected to land.
The country's first Moon mission - Chandrayaan-1, in 2008 - carried out the first and most detailed search for water on the lunar surface using radars.
Chandrayaan-2 entered the Moon's orbit on 20 August and was due to make a controlled descent to the surface early on Saturday, Indian time, over a month after it first took off.
Staff at mission control were glued to the screens at Isro's Bangalore space centre as the spacecraft made its descent towards the surface.
The control room burst into applause during the so-called rough breaking phase of the descent, with Prime Minister Modi watching the action from behind a glass screen.
Isro chairman Kailasavadivoo Sivan announced to staff that the ship's initial descent had been "normal," and that the mission's data would be analysed.
Mr Sivan had earlier described the final 15-minute descent period as "15 minutes of terror".
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