New Delhi: The US on May 10 said that Prime Minister Atal Behari Vajpayee's peace initiative can possibly lead to a step-by-step process for India and Pakistan to live as neighbours peacefully.

"I am cautiously optimistic," US Deputy Secretary of State Richard Armitage told reporters winding up his day-long confabulations with Indian leaders, including the Prime Minister, in New Delhi.

Armitage said one would like to see that relations between India and Pakistan improve and Vajpayee's initiative would lead to such a process. He also said that it would be a long process.

Asked about the problem of cross-border terrorism, Armitage said cross-border violence was a terrible thing and "all violence must end".

He said in his discussions both in Islamabad and Delhi the issue was discussed.

About his remarks in Islamabad that Pakistan President Pervez Musharraf had promised to wind up terrorist camps in Pakistan, he said the fact of the matter was that people were trying to do whatever they could.

The US envoy said he was told in Pakistan that more than 500 terrorists have been arrested there. Of them six were to have caused great harm to Americans in that country.

However, he said, India was a partner in the global war against terrorism.

PTI