Ross Taylor is batting at 67 and is accompanied by Tom Latham (3) at the crease.
The match will now be continued on Wednesday, when New Zealand is expected to resume its innings from the second ball of the 46th over.
Batting first in Manchester the Black Caps laboured their way to 211 for five before rain halted play in the 47th over.
However, former New Zealand captain Daniel Vettori had a more optimistic view of the Black Caps' situation.
The showers briefly relented at 5.30pm to raise hopes of completing the fixture, albeit with India facing a 20-over chase, but then returned, ensuring play will be deferred until Wednesday morning, weather permitting.
If a 20 overs per side match can not be completed on Wednesday as well, India would go through to Sunday´s final at Lord´s on the basis of having finished first to New Zealand´s fourth in the 10-team group stage. The Kiwis struggled to put runs on the board against some disciplined bowling by India. For India, Ravindra Jadeja was the standout performer, giving away just 34 runs from his 10 overs. India topped the league stage, while the Kiwis ended fourth.
That brought together Williamson and Taylor but even the two experienced hands could not turn the tide, a watchful stand of 65 in exactly 17 overs yielding only five fours.
O'Brien has defended New Zealand's approach on what he believes was a tough pitch to bat on.
Taylor successfully reviewed a leg-before decision off Bhuvneshwar on 52, having been hit outside the line of impact, before the players were hauled off after 46.1 overs as the inclement weather worsened. "To come back tomorrow, they will finish the game, it's the fair way to do it, and I think it makes India the favourites coming into tomorrow", he said on Cricinfo.
Tournament hosts England and reigning champions Australia will contest the second semi-final at Edgbaston on Thursday, with that match able to continue on to Friday if a reserve day is required.