The G20 communique issued at the end of a two-day summit in Brisbane declared that member nations would "begin to exchange information automatically with each other and with other countries by 2017 or end-2018".
Last year's annual summit in St Petersburg had declared that the nations "expect to begin to exchange information automatically on tax matters among G20 members by the end of 2015".
India has contended that the automatic exchange of information on bank accounts of foreign nationals in each country, proposed by the Organisation of Economic Cooperation and Development (OECD), will help it probe offenders faster.
Both the Modi and Manmohan Singh governments had argued in the Supreme Court that information on overseas accounts obtained through bilateral agreements with other nations - the tool India currently uses - comes with riders.
A key caveat in most of these pacts disallows India from making public the names of overseas account holders unless charges are registered against them.
"What we are trying as part of a G20 process is to have an automatic exchange of such information without making a request, because when you make a request you get caveats," foreign ministry spokesperson Syed Akbaruddin had said on Friday.
Modi has over the past two days pressed the 18 other nations and the European Union, which with India make up the G20, to speed up the process of adopting a global standard on tax-related information exchange that it could then pressure other nations to adopt.
"The Prime Minister made a strong pitch for repatriation of black money," railway minister and Modi's top G20 aide Suresh Prabhu said today.
"He said that it is very important. India is doing its level best to get it but because of certain rigidities, certain laws, certain situations that exist because of past treaties made many years ago...."
The G20 did indicate it would speed up work on reforming international tax laws, making it harder for international companies to avoid paying taxes through a strategy known as base erosion and profit-sharing (BEPS).
The OECD has been pushing for these reforms amid growing evidence that tax avoidance through BEPS is hurting emerging economies like India, Brazil and South Africa disproportionately.
The Brisbane meet agreed to finalise the road map for the reform of international tax laws in 2015.
But without the automatic exchange of taxation information, India cannot avoid the often long-winded diplomatic parleys it now needs to engage in to obtain overseas account details - even with caveats.
"Nations usually make up their minds on positions they will take at the G20 before their leaders land for the summit," an official who has travelled to more than one G20 meeting said.
"It isn't easy, even with a persuasive Prime Minister, to change minds over a two-day summit."
Crucially, the Brisbane G20 declaration adds a caveat to the implementation of the automatic exchange of information even by 2017 or end-2018. This, the document says, will be "subject to completing necessary legislative procedures".
Other officials hinted that while the delay was a setback at Modi's first ever G20 summit, it wasn't completely unexpected.
"The delay is disappointing, but I'm not surprised," an official who has been previously involved with international economic diplomacy said. "It's not a priority for this G20 -- even if we wish it were."
- The Telegraph, Calcutta