Kasab, 22, is currently lodged in the high security Arthur Road Jail in Mumbai.
"We welcome the verdict. It serves those who attacked Mumbai and India, considering it as a soft target," Patil said.
On the process of appeal in the high court against the verdict, Patil said, "We will request the Centre that the HC procedure should be fast tracked because charges against Kasab are serious."
On the special court dismissing all charges against two suspected co-conspirators, Fahim Ansari and Sabauddin Ahmed, in the 26/11 attack case, Patil said the government will appeal in HC against the ruling.
Patil said the judge sentenced Kasab to death by hanging on the counts of murder, abetting and conspiracy to murder; waging war against the state; and violating India's unlawful activities laws.
"All charges against him have been proved," he said.
Patil said international organisations should put pressure on Pakistan to hand over the 20 wanted accused in the 26/11 Mumbai terror attack trial to us.
Chief Minister Ashok Chavan said, "I am thankful to the court for taking such a fast decision."
Shiv Sena too expressed satisfaction at the death sentence to Kasab.
"We congratulate special public prosecutor Ujwal Nikam and the court," Sena spokesperson Neelam Gorhe said. This has been the fastest trial, 'however, mercy petition of Afzal Guru in the 2001 Parliament attack case is still pending. There is a need to implement judgements delivered through speedy justice system at the higher level urgently so that terrorists will be prevented from killing innocent people,' Gorhe said, adding the masterminds in 26/11 attacks are still free.
Welcoming the death sentence to Kasab, Crime Branch chief Himanshu Roy said, "In a fair, honest and transparent way we have shown the world that the charges we pressed against Kasab were true. They were proved in the court and he was awarded death sentence. With this, we have shown the world how Pakistan was involved in terror activities."
"We welcome the sentence. I feel it was a very important probe," Roy said, adding the verdict would send out a strong message to those thinking about terror activities against the country.
Congratulating ATS chief Rakesh Maria, the former Crime Branch chief who supervised the terror attacks probe, Additional Police Commissioner (Crime) Deven Bharti and their team, he said the judge has also complimented them for the manner in which they probed the case.
Roy said if the death penalty was challenged, they would surely face it.
Image: Maharashtra Home Minister R R Patil