The Indian Government has asked the Pakistan Government to extradite some of the top extremists, including Dawood Ibrahim and the LeT chief Maulana Masood Azhar, wanted in India for terrorist attacks on Indian soil. The Pakistani Government has predictably enough refused. Both countries have taken public stances on these issues and effectively boxed themselves into two corners from where a modus vivendi appears remote. The public quibbling over the veracity of the evidence incriminating these extremists is clearly a smokescreen to paper over the reality. We have a classic foreign policy stalemate.
Let us analyze the stalemate. In the face of mounting public opposition and evidence linking the Mumbai attacks to Pakistan, Indian Government has little choice but to demand action against the perpetrators, now freely moving within Pakistan. The continuing strong influence of the army and the counter-intelligence agency ISI in the domestic political balance of power in the country, ensures that it will be impossible for any Pakistani Government to hand over these terrorists to India. In fact, given the long and dirty history of the army and ISI using these extremists to forment civil strife in India, it will be suicidal for any Pakistani establishment (now or later) to hand over them.
In other words, India wants action taken against these terrorists while Pakistan cannot afford to let India lay its hands on these terrorists. These are core realities that cannot be wished away. We have a classic game theoretic framework, where two agents are facing each other with each one expecting the other to blink first. India threatens to go to war if its demand is not met, while Pakistan refuses to hand over the extremists. Any solution has to be achieved keeping in mind this contextual framework.
The only solution appears to be one where Pakistan puts these extremists under trial and take strong action against them (including if need be execution), without handing over them to India. This could satisfy both countries, without compromising on their core public positions. If the Pakistani Government is reluctant to put them under trial within the country, then they can be tried in a third country (like US). The trial and punishment to these elements will also go a long way in helping Pakistan make a break with its unsavoury past.
Incidentally, the army and intelligence agencies within many countries have a tried and tested method for disposing off such past friends who have now become liabilities - bump them off! Such instances, where the trial of rogue elements whose testimony can create domestic political problems within a country, highlights the utility of a formal international mechanism to facilitate secret trials in third countries.
All of this ofcourse pre-supposes that the Pakistani Government is no longer involved in supporting extremist activities in India. If Pakistan is continuing to provide material support for terrorism on Indian soil (and if this is true, then we can safely conclude that the army and other rogue elements are running the Pakistani State and the civilian Government is a mere facade), then it is different matter and it will be naive for the Indian Government to expect that diplomacy will achieve the desired objective. A military solution (either directly or through the US) will be the only alternative left. The other alternative would be for a Noreiga-style abduction of these extremists from Pakistani soil by Indian intelligence agents!
As an afterthought, by prevaricating and delaying, India may have closed the option of airstrikes on targets in Pakistan. This option was open, without too much international outcry, only in the immediate aftermath of the terrorist attacks. A surgical strike in the first couple of days could have passed through without mch international opposition.